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Category (mathematics)
In mathematics, a category is an algebraic structure that comprises "objects" that are linked by "arrows". A category has two basic properties: the ability to compose the arrows associatively and the existence of an identity arrow for each object. A simple example is the category of sets, whose objects are sets and whose arrows are functions. On the other hand, any monoid can be understood as a special sort of category, and so can any preorder. In general, the objects and arrows may be abstract entities of any kind, and the notion of category provides a fundamental and abstract way to describe mathematical entities and their relationships. This is the central idea of category theory, a branch of mathematics which seeks to generalize all of mathematics in terms of objects and arrows, independent of what the objects and arrows represent. Virtually every branch of modern mathematics can be described in terms of categories, and doing so often reveals deep insights and similarities between seemingly different areas of mathematics. For more extensive motivational background and historical notes, see category theory and the list of category theory topics.
This page contains text from Wikipedia, the Free Encyclopedia - https://wn.com/Category_(mathematics)
Category
Category, plural categories, may refer to:
Philosophy and general uses
Mathematics
- Abelian category
- Category of small categories
- Category of sets
- Category (topology) in the context of Baire spaces
- Lusternik–Schnirelmann category, sometimes called LS-category or simply category
- Monoidal category
- Preadditive category
Linguistics
This page contains text from Wikipedia, the Free Encyclopedia - https://wn.com/Category
Lusternik–Schnirelmann category
In mathematics, the Lyusternik–Schnirelmann category (or, Lusternik–Schnirelmann category, LS-category) of a topological space 
is the homotopical invariant defined to be the smallest integer number 
such that there is an open covering 
of with the property that each inclusion map 
is nullhomotopic. For example, if is the circle, this takes the value two.
Sometimes a different normalization of the invariant is adopted, which is one less than the definition above Such a normalization has been adopted in the definitive monograph by Cornea, Lupton, Oprea, and Tanré (see below).
In general it is not easy to compute this invariant, which was initially introduced by Lazar Lyusternik and Lev Schnirelmann in connection with variational problems. It has a close connection with algebraic topology, in particular cup-length. In the modern normalization, the cup-length is a lower bound for LS category.
It was, as originally defined for the case of X a manifold, the lower bound for the number of critical points that a real-valued function on X could possess (this should be compared with the result in Morse theory that shows that the sum of the Betti numbers is a lower bound for the number of critical points of a Morse function).
This page contains text from Wikipedia, the Free Encyclopedia - https://wn.com/Lusternik–Schnirelmann_category
Grammatical category
A grammatical category is a property of items within the grammar of a language; it has a number of possible values (sometimes called grammemes), which are normally mutually exclusive within a given category. Examples of frequently encountered grammatical categories include tense (which may take values such as present, past, etc.), number (with values such as singular, plural, and sometimes dual), and gender (with values such as masculine, feminine and neuter).
Although terminology is not always consistent, a distinction should be made between these grammatical categories (tense, number, etc.) and lexical categories, which are closely synonymous with the traditional parts of speech (noun, verb, adjective, etc.), or more generally syntactic categories. Grammatical categories are also referred to as (grammatical) features.
The name given to a grammatical category (as an uncountable noun) is generally also used (as a countable noun) to denote any of the possible values for that category. For example, the values available in a given language for the category "tense" are called "tenses", the values available for the category "gender" are called "genders", and so on.
This page contains text from Wikipedia, the Free Encyclopedia - https://wn.com/Grammatical_category
Theory
Theory is a contemplative and rational type of abstract or generalizing thinking, or the results of such thinking. Depending on the context, the results might for example include generalized explanations of how nature works. The word has its roots in ancient Greek, but in modern use it has taken on several different related meanings. A theory is not the same as a hypothesis. A theory provides an explanatory framework for some observation, and from the assumptions of the explanation follows a number of possible hypotheses that can be tested in order to provide support for, or challenge, the theory.
A theory can be normative (or prescriptive), meaning a postulation about what ought to be. It provides "goals, norms, and standards". A theory can be a body of knowledge, which may or may not be associated with particular explanatory models. To theorize is to develop this body of knowledge.
As already in Aristotle's definitions, theory is very often contrasted to "practice" (from Greek praxis, πρᾶξις) a Greek term for "doing", which is opposed to theory because pure theory involves no doing apart from itself. A classical example of the distinction between "theoretical" and "practical" uses the discipline of medicine: medical theory involves trying to understand the causes and nature of health and sickness, while the practical side of medicine is trying to make people healthy. These two things are related but can be independent, because it is possible to research health and sickness without curing specific patients, and it is possible to cure a patient without knowing how the cure worked.
This page contains text from Wikipedia, the Free Encyclopedia - https://wn.com/Theory
Chess theory
The game of chess is commonly divided into three phases: the opening, middlegame, and endgame. There is a large body of theory regarding how the game should be played in each of these phases, especially the opening and endgame. Those who write about chess theory, who are often but not necessarily also eminent players, are referred to as "theorists" or "theoreticians".
"Opening theory" commonly refers to consensus, broadly represented by current literature on the openings. "Endgame theory" consists of statements regarding specific positions, or positions of a similar type, though there are few universally applicable principles. "Middlegame theory" often refers to maxims or principles applicable to the middlegame. The modern trend, however, is to assign paramount importance to analysis of the specific position at hand rather than to general principles.
The development of theory in all of these areas has been assisted by the vast literature on the game. In 1913, preeminent chess historian H. J. R. Murray wrote in his 900-page magnum opus A History of Chess that, "The game possesses a literature which in contents probably exceeds that of all other games combined." He estimated that at that time the "total number of books on chess, chess magazines, and newspapers devoting space regularly to the game probably exceeds 5,000". In 1949, B. H. Wood opined that the number had increased to about 20,000.David Hooper and Kenneth Whyld wrote in 1992 that, "Since then there has been a steady increase year by year of the number of new chess publications. No one knows how many have been printed..." The world's largest chess library, the John G. White Collection at the Cleveland Public Library, contains over 32,000 chess books and serials, including over 6,000 bound volumes of chess periodicals. Chess players today also avail themselves of computer-based sources of information.
This page contains text from Wikipedia, the Free Encyclopedia - https://wn.com/Chess_theory
Scientific theory
A scientific theory is a well-substantiated explanation of some aspect of the natural world that is acquired through the scientific method and repeatedly tested and confirmed through observation and experimentation. As with most (if not all) forms of scientific knowledge, scientific theories are inductive in nature and aim for predictive power and explanatory capability.
The strength of a scientific theory is related to the diversity of phenomena it can explain, and to its elegance and simplicity. See Occam's razor. As additional scientific evidence is gathered, a scientific theory may be rejected or modified if it does not fit the new empirical findings; in such circumstances, a more accurate theory is then desired. In certain cases, the less-accurate unmodified scientific theory can still be treated as a theory if it is useful (due to its sheer simplicity) as an approximation under specific conditions (e.g., Newton's laws of motion as an approximation to special relativity at velocities which are small relative to the speed of light).
This page contains text from Wikipedia, the Free Encyclopedia - https://wn.com/Scientific_theory
Podcasts:
-
What is Category Theory in mathematics? Johns Hopkins' Dr. Emily Riehl explains
The President's Frontier Award was established with a $2.5 million donation from trustee Louis J. Forster. Forster helped design the award to support exceptional scholars among the Johns Hopkins faculty who are on the cusp of transforming their fields. The award recognizes one person each year with $250,000 in funding for their work. This PFA lecture features 2020 recipient Dr. Emily Riehl presenting on Category Theory. Thinking categorically can help serve as a guide post as you trek the grand scheme of (mathematical) things. As written in Quanta Magazine in a 2020 interview with Riehl, “category theory and its next-generation version, higher category theory, are central to many fields of math, from algebraic geometry to mathematical physics. In those areas, Riehl said, ‘I think it wou...
published: 16 Dec 2020 -
What is Category Theory?
published: 05 Jan 2018 -
The Map of Mathematics
The entire field of mathematics summarised in a single map! This shows how pure mathematics and applied mathematics relate to each other and all of the sub-topics they are made from. #mathematics #DomainOfScience If you would like to buy a poster of this map, they are available here: North America: https://store.dftba.com/products/map-of-mathematics-poster Everywhere else: http://www.redbubble.com/people/dominicwalliman/works/25095968-the-map-of-mathematics French version: https://www.redbubble.com/people/dominicwalliman/works/40572671-the-map-of-mathematics-french-version?asc=u Spanish Version: https://www.redbubble.com/people/dominicwalliman/works/40572693-the-map-of-mathematics-spanish-version?asc=u I have also made a version available for educational use which you can find here: ht...
published: 01 Feb 2017 -
Category Theory For Beginners: Introduction
Category theory is close to the perfect language. It can be used to describe many mathematical ideas, and see the relations between them, and their deeper structure. This is the first video in a course where we will carefully introduce the main ideas of category theory, and motivate them with lots of applications. This first video gives the definition of a category and give some motivation for studying the subject. In particular we define a category, give the definition of a monoid, we define a pre-ordered set (preorder), we define the category Set, of sets and functions. We introduce functional programming. We define the final object (terminal object), and explain how the ideas can be used to do set theory without considering the elements within sets directly. Some people have said they ...
published: 13 May 2019 -
What is Category (mathematics)?, Explain Category (mathematics), Define Category (mathematics)
~~~ Category (mathematics) ~~~ Title: What is Category (mathematics)?, Explain Category (mathematics), Define Category (mathematics) Created on: 2018-07-11 Source Link: https://en.wikipedia.org/wiki/Category_(mathematics) ------ Description: In mathematics, a category is an algebraic structure similar to a group but without requiring inverse or closure properties. It comprises "objects" that are linked by "arrows". A category has two basic properties: the ability to compose the arrows associatively and the existence of an identity arrow for each object. A simple example is the category of sets, whose objects are sets and whose arrows are functions. Category theory is a branch of mathematics that seeks to generalize all of mathematics in terms of categories, independent of what their obj...
published: 11 Jul 2018 -
Category Theory: Visual Mathematics for the 21st century
RCON 3 Day 3 track 4 Session 4 Category Theory: Visual Mathematics for the 21st century by Jamie Vicary
published: 14 Sep 2018 -
ACT@UCR Seminar: Mathematics in the 21st Century - John Baez
The global warming crisis is part of a bigger transformation in which humanity realizes that the Earth is a finite system and that our population, energy usage, and the like cannot continue to grow exponentially. If civilization survives this transformation, it will affect mathematics – and be affected by it – just as dramatically as the agricultural revolution or industrial revolution. We should get ready! slides: http://math.ucr.edu/home/baez/planet/planet_ucr.pdf This talk is part of the Applied Category Theory at U. C. Riverside Seminar: : https://johncarlosbaez.wordpress.com/2018/12/14/applied-category-theory-seminar/ Edited by Paola Fernandez
published: 13 Jan 2019 -
Emily Riehl on Topology, Categories, and the Future of Mathematics
Patreon: https://www.patreon.com/seanmcarroll Blog post with audio player, show notes, and transcript: https://www.preposterousuniverse.com/podcast/2021/05/10/146-emily-riehl-on-topology-categories-and-the-future-of-mathematics/ “A way that math can make the world a better place is by making it a more interesting place to be a conscious being.” So says mathematician Emily Riehl near the start of this episode, and it’s a good summary of what’s to come. Emily works in realms of topology and category theory that are far away from practical applications, or even to some non-practical areas of theoretical physics. But they help us think about what is possible and how everything fits together, and what’s more interesting than that? We talk about what topology is, the specific example of homotop...
published: 10 May 2021 -
Category (mathematics)
If you find our videos helpful you can support us by buying something from amazon. https://www.amazon.com/?tag=wiki-audio-20 Category (mathematics) In mathematics, a category is an algebraic structure that comprises "objects" that are linked by "arrows".A category has two basic properties: the ability to compose the arrows associatively and the existence of an identity arrow for each object. =======Image-Copyright-Info======== License: Creative Commons Attribution-Share Alike 4.0 (CC BY-SA 4.0) LicenseLink: http://creativecommons.org/licenses/by-sa/4.0 Author-Info: IkamusumeFan Image Source: https://en.wikipedia.org/wiki/File:Category_SVG.svg =======Image-Copyright-Info======== -Video is targeted to blind users Attribution: Article text available under CC-BY-SA image source in...
published: 22 Jan 2016 -
Classification/ branches of mathematics | Application | Useful maths | Learning | Mathsfun
Hello everyone!! Iss video me classification/ branches of maths ke baare me discuss kiya hai. Iss baar kuch alag try kiya hai so agar aapko pasand aaye to please comment below. If you have any query or doubts then please comment or dm to instagram. Instagram - mr.rajveer07 #classification #maths #branchesofmaths #stayhome #staysafe #mathsfun #learning in new way #mathsmeme #application #mathematics Thank you so much for watching
published: 25 May 2020
developed with YouTube
56:34
What is Category Theory in mathematics? Johns Hopkins' Dr. Emily Riehl explains
- Order: Reorder
- Duration: 56:34
- Uploaded Date: 16 Dec 2020
- views: 40642
The President's Frontier Award was established with a $2.5 million donation from trustee Louis J. Forster. Forster helped design the award to support exceptiona...
The President's Frontier Award was established with a $2.5 million donation from trustee Louis J. Forster. Forster helped design the award to support exceptional scholars among the Johns Hopkins faculty who are on the cusp of transforming their fields. The award recognizes one person each year with $250,000 in funding for their work.
This PFA lecture features 2020 recipient Dr. Emily Riehl presenting on Category Theory. Thinking categorically can help serve as a guide post as you trek the grand scheme of (mathematical) things. As written in Quanta Magazine in a 2020 interview with Riehl, “category theory and its next-generation version, higher category theory, are central to many fields of math, from algebraic geometry to mathematical physics. In those areas, Riehl said, ‘I think it would be impossible to describe the kind of basic objects of study without categorical language.’”
Join us for this fantastic event honoring the brilliant work of Dr. Riehl, opened by Provost Sunil Kumar and Dr. John Toscano. Denis Wirtz, Vice Provost for Research, provides closing remarks. To learn more, visit jhu.edu/hopkinsathome
https://wn.com/What_Is_Category_Theory_In_Mathematics_Johns_Hopkins'_Dr._Emily_Riehl_Explains
The President's Frontier Award was established with a $2.5 million donation from trustee Louis J. Forster. Forster helped design the award to support exceptional scholars among the Johns Hopkins faculty who are on the cusp of transforming their fields. The award recognizes one person each year with $250,000 in funding for their work.
This PFA lecture features 2020 recipient Dr. Emily Riehl presenting on Category Theory. Thinking categorically can help serve as a guide post as you trek the grand scheme of (mathematical) things. As written in Quanta Magazine in a 2020 interview with Riehl, “category theory and its next-generation version, higher category theory, are central to many fields of math, from algebraic geometry to mathematical physics. In those areas, Riehl said, ‘I think it would be impossible to describe the kind of basic objects of study without categorical language.’”
Join us for this fantastic event honoring the brilliant work of Dr. Riehl, opened by Provost Sunil Kumar and Dr. John Toscano. Denis Wirtz, Vice Provost for Research, provides closing remarks. To learn more, visit jhu.edu/hopkinsathome
6:19
What is Category Theory?
- Order: Reorder
- Duration: 6:19
- Uploaded Date: 05 Jan 2018
- views: 64820
- published: 05 Jan 2018
- views: 64820
11:06
The Map of Mathematics
- Order: Reorder
- Duration: 11:06
- Uploaded Date: 01 Feb 2017
- views: 14122400
The entire field of mathematics summarised in a single map! This shows how pure mathematics and applied mathematics relate to each other and all of the sub-topi...
The entire field of mathematics summarised in a single map! This shows how pure mathematics and applied mathematics relate to each other and all of the sub-topics they are made from.
#mathematics #DomainOfScience
If you would like to buy a poster of this map, they are available here:
North America: https://store.dftba.com/products/map-of-mathematics-poster
Everywhere else: http://www.redbubble.com/people/dominicwalliman/works/25095968-the-map-of-mathematics
French version: https://www.redbubble.com/people/dominicwalliman/works/40572671-the-map-of-mathematics-french-version?asc=u
Spanish Version: https://www.redbubble.com/people/dominicwalliman/works/40572693-the-map-of-mathematics-spanish-version?asc=u
I have also made a version available for educational use which you can find here: https://www.flickr.com/photos/95869671@N08/32264483720/in/dateposted-public/
To err is to human, and I human a lot. I always try my best to be as correct as possible, but unfortunately I make mistakes. This is the errata where I correct my silly mistakes. My goal is to one day do a video with no errors!
1. The number one is not a prime number. The definition of a prime number is a number can be divided evenly only by 1, or itself. And it must be a whole number GREATER than 1. (This last bit is the bit I forgot).
2. In the trigonometry section I drew cos(theta) = opposite / adjacent. This is the kind of thing you learn in high school and guess what. I got it wrong! Dummy. It should be cos(theta) = adjacent / hypotenuse.
3. My drawing of dice is slightly wrong. Most dice have their opposite sides adding up to 7, so when I drew 3 and 4 next to each other that is incorrect.
4. I said that the Gödel Incompleteness Theorems implied that mathematics is made up by humans, but that is wrong, just ignore that statement. I have learned more about it now, here is a good video explaining it: https://youtu.be/O4ndIDcDSGc
5. In the animation about imaginary numbers I drew the real axis as vertical and the imaginary axis as horizontal which is opposite to the conventional way it is done.
Thanks so much to my supporters on Patreon. I hope to make money from my videos one day, but I’m not there yet! If you enjoy my videos and would like to help me make more this is the best way and I appreciate it very much. https://www.patreon.com/domainofscience
Here are links to some of the sources I used in this video.
Links:
Summary of mathematics: https://en.wikipedia.org/wiki/Mathematics
Earliest human counting: http://mathtimeline.weebly.com/early-human-counting-tools.html
First use of zero: https://en.wikipedia.org/wiki/0#History http://www.livescience.com/27853-who-invented-zero.html
First use of negative numbers: https://www.quora.com/Who-is-the-inventor-of-negative-numbers
Renaissance science: https://en.wikipedia.org/wiki/History_of_science_in_the_Renaissance
History of complex numbers: http://rossroessler.tripod.com/ https://en.wikipedia.org/wiki/Mathematics
Proof that pi is irrational: https://www.quora.com/How-do-you-prove-that-pi-is-an-irrational-number
and https://en.wikipedia.org/wiki/Proof_that_%CF%80_is_irrational#Laczkovich.27s_proof
Also, if you enjoyed this video, you will probably like my science books, available in all good books shops around the work and is printed in 16 languages. Links are below or just search for Professor Astro Cat. They are fun children's books aimed at the age range 7-12. But they are also a hit with adults who want good explanations of science. The books have won awards and the app won a Webby.
Frontiers of Space: http://nobrow.net/shop/professor-astro-cats-frontiers-of-space/
Atomic Adventure: http://nobrow.net/shop/professor-astro-cats-atomic-adventure/
Intergalactic Activity Book: http://nobrow.net/shop/professor-astro-cats-intergalactic-activity-book/
Solar System App: http://www.minilabstudios.com/apps/professor-astro-cats-solar-system/
Find me on twitter, instagram, and my website:
http://dominicwalliman.com
https://twitter.com/DominicWalliman
https://www.instagram.com/dominicwalliman
https://www.facebook.com/dominicwalliman
https://wn.com/The_Map_Of_Mathematics
The entire field of mathematics summarised in a single map! This shows how pure mathematics and applied mathematics relate to each other and all of the sub-topics they are made from.
#mathematics #DomainOfScience
If you would like to buy a poster of this map, they are available here:
North America: https://store.dftba.com/products/map-of-mathematics-poster
Everywhere else: http://www.redbubble.com/people/dominicwalliman/works/25095968-the-map-of-mathematics
French version: https://www.redbubble.com/people/dominicwalliman/works/40572671-the-map-of-mathematics-french-version?asc=u
Spanish Version: https://www.redbubble.com/people/dominicwalliman/works/40572693-the-map-of-mathematics-spanish-version?asc=u
I have also made a version available for educational use which you can find here: https://www.flickr.com/photos/95869671@N08/32264483720/in/dateposted-public/
To err is to human, and I human a lot. I always try my best to be as correct as possible, but unfortunately I make mistakes. This is the errata where I correct my silly mistakes. My goal is to one day do a video with no errors!
1. The number one is not a prime number. The definition of a prime number is a number can be divided evenly only by 1, or itself. And it must be a whole number GREATER than 1. (This last bit is the bit I forgot).
2. In the trigonometry section I drew cos(theta) = opposite / adjacent. This is the kind of thing you learn in high school and guess what. I got it wrong! Dummy. It should be cos(theta) = adjacent / hypotenuse.
3. My drawing of dice is slightly wrong. Most dice have their opposite sides adding up to 7, so when I drew 3 and 4 next to each other that is incorrect.
4. I said that the Gödel Incompleteness Theorems implied that mathematics is made up by humans, but that is wrong, just ignore that statement. I have learned more about it now, here is a good video explaining it: https://youtu.be/O4ndIDcDSGc
5. In the animation about imaginary numbers I drew the real axis as vertical and the imaginary axis as horizontal which is opposite to the conventional way it is done.
Thanks so much to my supporters on Patreon. I hope to make money from my videos one day, but I’m not there yet! If you enjoy my videos and would like to help me make more this is the best way and I appreciate it very much. https://www.patreon.com/domainofscience
Here are links to some of the sources I used in this video.
Links:
Summary of mathematics: https://en.wikipedia.org/wiki/Mathematics
Earliest human counting: http://mathtimeline.weebly.com/early-human-counting-tools.html
First use of zero: https://en.wikipedia.org/wiki/0#History http://www.livescience.com/27853-who-invented-zero.html
First use of negative numbers: https://www.quora.com/Who-is-the-inventor-of-negative-numbers
Renaissance science: https://en.wikipedia.org/wiki/History_of_science_in_the_Renaissance
History of complex numbers: http://rossroessler.tripod.com/ https://en.wikipedia.org/wiki/Mathematics
Proof that pi is irrational: https://www.quora.com/How-do-you-prove-that-pi-is-an-irrational-number
and https://en.wikipedia.org/wiki/Proof_that_%CF%80_is_irrational#Laczkovich.27s_proof
Also, if you enjoyed this video, you will probably like my science books, available in all good books shops around the work and is printed in 16 languages. Links are below or just search for Professor Astro Cat. They are fun children's books aimed at the age range 7-12. But they are also a hit with adults who want good explanations of science. The books have won awards and the app won a Webby.
Frontiers of Space: http://nobrow.net/shop/professor-astro-cats-frontiers-of-space/
Atomic Adventure: http://nobrow.net/shop/professor-astro-cats-atomic-adventure/
Intergalactic Activity Book: http://nobrow.net/shop/professor-astro-cats-intergalactic-activity-book/
Solar System App: http://www.minilabstudios.com/apps/professor-astro-cats-solar-system/
Find me on twitter, instagram, and my website:
http://dominicwalliman.com
https://twitter.com/DominicWalliman
https://www.instagram.com/dominicwalliman
https://www.facebook.com/dominicwalliman
- published: 01 Feb 2017
- views: 14122400
57:56
Category Theory For Beginners: Introduction
- Order: Reorder
- Duration: 57:56
- Uploaded Date: 13 May 2019
- views: 90436
Category theory is close to the perfect language. It can be used to describe many mathematical ideas, and see the relations between them, and their deeper struc...
Category theory is close to the perfect language. It can be used to describe many mathematical ideas, and see the relations between them, and their deeper structure. This is the first video in a course where we will carefully introduce the main ideas of category theory, and motivate them with lots of applications. This first video gives the definition of a category and give some motivation for studying the subject. In particular we define a category, give the definition of a monoid, we define a pre-ordered set (preorder), we define the category Set, of sets and functions. We introduce functional programming. We define the final object (terminal object), and explain how the ideas can be used to do set theory without considering the elements within sets directly.
Some people have said they want to support my efforts to make educational videos and software, and so I have made a Patreon page
https://www.patreon.com/richardsouthwell
Any support would really help me produce more videos and software.
https://wn.com/Category_Theory_For_Beginners_Introduction
Category theory is close to the perfect language. It can be used to describe many mathematical ideas, and see the relations between them, and their deeper structure. This is the first video in a course where we will carefully introduce the main ideas of category theory, and motivate them with lots of applications. This first video gives the definition of a category and give some motivation for studying the subject. In particular we define a category, give the definition of a monoid, we define a pre-ordered set (preorder), we define the category Set, of sets and functions. We introduce functional programming. We define the final object (terminal object), and explain how the ideas can be used to do set theory without considering the elements within sets directly.
Some people have said they want to support my efforts to make educational videos and software, and so I have made a Patreon page
https://www.patreon.com/richardsouthwell
Any support would really help me produce more videos and software.
- published: 13 May 2019
- views: 90436
2:47
What is Category (mathematics)?, Explain Category (mathematics), Define Category (mathematics)
- Order: Reorder
- Duration: 2:47
- Uploaded Date: 11 Jul 2018
- views: 1813
~~~ Category (mathematics) ~~~
Title: What is Category (mathematics)?, Explain Category (mathematics), Define Category (mathematics)
Created on: 2018-07-11
Sou...
~~~ Category (mathematics) ~~~
Title: What is Category (mathematics)?, Explain Category (mathematics), Define Category (mathematics)
Created on: 2018-07-11
Source Link: https://en.wikipedia.org/wiki/Category_(mathematics)
------
Description: In mathematics, a category is an algebraic structure similar to a group but without requiring inverse or closure properties. It comprises "objects" that are linked by "arrows". A category has two basic properties: the ability to compose the arrows associatively and the existence of an identity arrow for each object. A simple example is the category of sets, whose objects are sets and whose arrows are functions. Category theory is a branch of mathematics that seeks to generalize all of mathematics in terms of categories, independent of what their objects and arrows represent. Virtually every branch of modern mathematics can be described in terms of categories, and doing so often reveals deep insights and similarities between seemingly different areas of mathematics. As such, category theory provides an alternative foundation for mathematics to set theory and other proposed axiomatic foundations. In general, the objects and arrows may be abstract entities of any kind, and the notion of category provides a fundamental and abstract way to describe mathematical entities and their relationships. In addition to formalizing mathematics, category theory is also used to formalize many other systems in computer science, such as the semantics of programming languages. Two categories are the same if they have the same collection of objects, the same collection of arrows, and the same associative method of composing any pair of arrows. Two different categories may also be considered "equivalent" for purposes of category theory, even if they do not have precisely the same structure. Well-known categories are denoted by a short capitalized word or abbreviation in bold or italics: examples include Set, the category of sets and set functions; Ring, the category of rings and ring homomorphisms; and Top, the category of topological spaces and continuous maps. All of the preceding categories have the identity map as identity arrow and composition as the associative operation on arrows. The classic and still much used text on category theory is Categories for the Working Mathematician by Saunders Mac Lane. Other references are given in the References below. The basic definitions in this article are contained within the first few chapters of any of these books. Any monoid can be understood as a special sort of category , and so can any preorder.
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https://wn.com/What_Is_Category_(Mathematics)_,_Explain_Category_(Mathematics),_Define_Category_(Mathematics)
~~~ Category (mathematics) ~~~
Title: What is Category (mathematics)?, Explain Category (mathematics), Define Category (mathematics)
Created on: 2018-07-11
Source Link: https://en.wikipedia.org/wiki/Category_(mathematics)
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Description: In mathematics, a category is an algebraic structure similar to a group but without requiring inverse or closure properties. It comprises "objects" that are linked by "arrows". A category has two basic properties: the ability to compose the arrows associatively and the existence of an identity arrow for each object. A simple example is the category of sets, whose objects are sets and whose arrows are functions. Category theory is a branch of mathematics that seeks to generalize all of mathematics in terms of categories, independent of what their objects and arrows represent. Virtually every branch of modern mathematics can be described in terms of categories, and doing so often reveals deep insights and similarities between seemingly different areas of mathematics. As such, category theory provides an alternative foundation for mathematics to set theory and other proposed axiomatic foundations. In general, the objects and arrows may be abstract entities of any kind, and the notion of category provides a fundamental and abstract way to describe mathematical entities and their relationships. In addition to formalizing mathematics, category theory is also used to formalize many other systems in computer science, such as the semantics of programming languages. Two categories are the same if they have the same collection of objects, the same collection of arrows, and the same associative method of composing any pair of arrows. Two different categories may also be considered "equivalent" for purposes of category theory, even if they do not have precisely the same structure. Well-known categories are denoted by a short capitalized word or abbreviation in bold or italics: examples include Set, the category of sets and set functions; Ring, the category of rings and ring homomorphisms; and Top, the category of topological spaces and continuous maps. All of the preceding categories have the identity map as identity arrow and composition as the associative operation on arrows. The classic and still much used text on category theory is Categories for the Working Mathematician by Saunders Mac Lane. Other references are given in the References below. The basic definitions in this article are contained within the first few chapters of any of these books. Any monoid can be understood as a special sort of category , and so can any preorder.
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Support: Donations can be made from https://wikimediafoundation.org/wiki/Ways_to_Give to support Wikimedia Foundation and knowledge sharing.
- published: 11 Jul 2018
- views: 1813
55:10
Category Theory: Visual Mathematics for the 21st century
- Order: Reorder
- Duration: 55:10
- Uploaded Date: 14 Sep 2018
- views: 1704
RCON 3 Day 3 track 4 Session 4
Category Theory: Visual Mathematics for the 21st century by Jamie Vicary
RCON 3 Day 3 track 4 Session 4
Category Theory: Visual Mathematics for the 21st century by Jamie Vicary
https://wn.com/Category_Theory_Visual_Mathematics_For_The_21St_Century
RCON 3 Day 3 track 4 Session 4
Category Theory: Visual Mathematics for the 21st century by Jamie Vicary
- published: 14 Sep 2018
- views: 1704
1:09:46
ACT@UCR Seminar: Mathematics in the 21st Century - John Baez
- Order: Reorder
- Duration: 1:09:46
- Uploaded Date: 13 Jan 2019
- views: 3767
The global warming crisis is part of a bigger transformation in which humanity realizes that the Earth is a finite system and that our population, energy usage,...
The global warming crisis is part of a bigger transformation in which humanity realizes that the Earth is a finite system and that our population, energy usage, and the like cannot continue to grow exponentially. If civilization survives this transformation, it will affect mathematics – and be affected by it – just as dramatically as the agricultural revolution or industrial revolution. We should get ready!
slides: http://math.ucr.edu/home/baez/planet/planet_ucr.pdf
This talk is part of the Applied Category Theory at U. C. Riverside Seminar: : https://johncarlosbaez.wordpress.com/2018/12/14/applied-category-theory-seminar/
Edited by Paola Fernandez
https://wn.com/Act_Ucr_Seminar_Mathematics_In_The_21St_Century_John_Baez
The global warming crisis is part of a bigger transformation in which humanity realizes that the Earth is a finite system and that our population, energy usage, and the like cannot continue to grow exponentially. If civilization survives this transformation, it will affect mathematics – and be affected by it – just as dramatically as the agricultural revolution or industrial revolution. We should get ready!
slides: http://math.ucr.edu/home/baez/planet/planet_ucr.pdf
This talk is part of the Applied Category Theory at U. C. Riverside Seminar: : https://johncarlosbaez.wordpress.com/2018/12/14/applied-category-theory-seminar/
Edited by Paola Fernandez
- published: 13 Jan 2019
- views: 3767
1:16:51
Emily Riehl on Topology, Categories, and the Future of Mathematics
- Order: Reorder
- Duration: 1:16:51
- Uploaded Date: 10 May 2021
- views: 21094
Patreon: https://www.patreon.com/seanmcarroll
Blog post with audio player, show notes, and transcript: https://www.preposterousuniverse.com/podcast/2021/05/10/1...
Patreon: https://www.patreon.com/seanmcarroll
Blog post with audio player, show notes, and transcript: https://www.preposterousuniverse.com/podcast/2021/05/10/146-emily-riehl-on-topology-categories-and-the-future-of-mathematics/
“A way that math can make the world a better place is by making it a more interesting place to be a conscious being.” So says mathematician Emily Riehl near the start of this episode, and it’s a good summary of what’s to come. Emily works in realms of topology and category theory that are far away from practical applications, or even to some non-practical areas of theoretical physics. But they help us think about what is possible and how everything fits together, and what’s more interesting than that? We talk about what topology is, the specific example of homotopy — how things deform into other things — and how thinking about that leads us into groups, rings, groupoids, and ultimately to category theory, the most abstract of them all.
Emily Riehl received a Ph.D in mathematics from the University of Chicago. She is currently an associate professor of mathematics at Johns Hopkins University. Among her honors are the JHU President’s Frontier Award and the Joan & Joseph Birman Research Prize. She is author of Categorical Homotopy Theory, and co-author of the upcoming Elements of ∞-Category Theory. She competed on the United States women’s national Australian rules football team, where she served as vice-captain.
Mindscape Podcast playlist: https://www.youtube.com/playlist?list=PLrxfgDEc2NxY_fRExpDXr87tzRbPCaA5x
#podcast #ideas #science #philosophy #culture
https://wn.com/Emily_Riehl_On_Topology,_Categories,_And_The_Future_Of_Mathematics
Patreon: https://www.patreon.com/seanmcarroll
Blog post with audio player, show notes, and transcript: https://www.preposterousuniverse.com/podcast/2021/05/10/146-emily-riehl-on-topology-categories-and-the-future-of-mathematics/
“A way that math can make the world a better place is by making it a more interesting place to be a conscious being.” So says mathematician Emily Riehl near the start of this episode, and it’s a good summary of what’s to come. Emily works in realms of topology and category theory that are far away from practical applications, or even to some non-practical areas of theoretical physics. But they help us think about what is possible and how everything fits together, and what’s more interesting than that? We talk about what topology is, the specific example of homotopy — how things deform into other things — and how thinking about that leads us into groups, rings, groupoids, and ultimately to category theory, the most abstract of them all.
Emily Riehl received a Ph.D in mathematics from the University of Chicago. She is currently an associate professor of mathematics at Johns Hopkins University. Among her honors are the JHU President’s Frontier Award and the Joan & Joseph Birman Research Prize. She is author of Categorical Homotopy Theory, and co-author of the upcoming Elements of ∞-Category Theory. She competed on the United States women’s national Australian rules football team, where she served as vice-captain.
Mindscape Podcast playlist: https://www.youtube.com/playlist?list=PLrxfgDEc2NxY_fRExpDXr87tzRbPCaA5x
#podcast #ideas #science #philosophy #culture
- published: 10 May 2021
- views: 21094
11:45
Category (mathematics)
- Order: Reorder
- Duration: 11:45
- Uploaded Date: 22 Jan 2016
- views: 519
If you find our videos helpful you can support us by buying something from amazon.
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Category (mathematics)
In mathe...
If you find our videos helpful you can support us by buying something from amazon.
https://www.amazon.com/?tag=wiki-audio-20
Category (mathematics)
In mathematics, a category is an algebraic structure that comprises "objects" that are linked by "arrows".A category has two basic properties: the ability to compose the arrows associatively and the existence of an identity arrow for each object.
=======Image-Copyright-Info========
License: Creative Commons Attribution-Share Alike 4.0 (CC BY-SA 4.0)
LicenseLink: http://creativecommons.org/licenses/by-sa/4.0
Author-Info: IkamusumeFan
Image Source: https://en.wikipedia.org/wiki/File:Category_SVG.svg
=======Image-Copyright-Info========
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https://wn.com/Category_(Mathematics)
If you find our videos helpful you can support us by buying something from amazon.
https://www.amazon.com/?tag=wiki-audio-20
Category (mathematics)
In mathematics, a category is an algebraic structure that comprises "objects" that are linked by "arrows".A category has two basic properties: the ability to compose the arrows associatively and the existence of an identity arrow for each object.
=======Image-Copyright-Info========
License: Creative Commons Attribution-Share Alike 4.0 (CC BY-SA 4.0)
LicenseLink: http://creativecommons.org/licenses/by-sa/4.0
Author-Info: IkamusumeFan
Image Source: https://en.wikipedia.org/wiki/File:Category_SVG.svg
=======Image-Copyright-Info========
-Video is targeted to blind users
Attribution:
Article text available under CC-BY-SA
image source in video
https://www.youtube.com/watch?v=kafQy7Xk4IQ
- published: 22 Jan 2016
- views: 519
7:13
Classification/ branches of mathematics | Application | Useful maths | Learning | Mathsfun
- Order: Reorder
- Duration: 7:13
- Uploaded Date: 25 May 2020
- views: 35952
Hello everyone!!
Iss video me classification/ branches of maths ke baare me discuss kiya hai.
Iss baar kuch alag try kiya hai so agar aapko pasand aaye to plea...
Hello everyone!!
Iss video me classification/ branches of maths ke baare me discuss kiya hai.
Iss baar kuch alag try kiya hai so agar aapko pasand aaye to please comment below.
If you have any query or doubts then please comment or dm to instagram.
Instagram - mr.rajveer07
#classification
#maths #branchesofmaths
#stayhome #staysafe
#mathsfun
#learning in new way
#mathsmeme
#application #mathematics
Thank you so much for watching
https://wn.com/Classification_Branches_Of_Mathematics_|_Application_|_Useful_Maths_|_Learning_|_Mathsfun
Hello everyone!!
Iss video me classification/ branches of maths ke baare me discuss kiya hai.
Iss baar kuch alag try kiya hai so agar aapko pasand aaye to please comment below.
If you have any query or doubts then please comment or dm to instagram.
Instagram - mr.rajveer07
#classification
#maths #branchesofmaths
#stayhome #staysafe
#mathsfun
#learning in new way
#mathsmeme
#application #mathematics
Thank you so much for watching
- published: 25 May 2020
- views: 35952
-
A Sensible Introduction to Category Theory
Remember when I used a video with a coconut in the thumbnail to drive a stake through the heart of mathematical structure? Today, in this introduction to the basics of category theory, I attempt to remove it. 27 Unhelpful Facts About Category Theory: https://www.youtube.com/watch?v=H0Ek86IH-3Y MetaMaths on category theory: https://www.youtube.com/watch?v=ZG6t0-JMrw0 My dissertation on the equivalence between the category of monoidal categories and the category of representable multicategories: https://drive.google.com/file/d/1hAkV1qSnUutzQMMQi48yo_fXsgb1YnbL/view?usp=sharing FURTHER READING Basic Category Theory (Tom Leinster): https://arxiv.org/pdf/1612.09375.pdf Categories for the Working Mathematician (Saunders Mac Lane): http://www.mtm.ufsc.br/~ebatista/2016-2/maclanecat.pdf Catego...
published: 22 Jun 2022 -
'Category Is...' Performance w/ Peppermint, Sasha, Trinity & Shea 👯♀️ | RuPaul's Drag Race Season 9
Start the music and gag over Peppermint, Sasha Velour, Trinity Taylor, and Shea Coulee during the 'Category Is' Challenge on RuPaul’s Drag Race Season 9. #VH1 #DragRace More from RuPaul's Drag Race: Official Website: http://www.vh1.com/shows/rupauls-drag-race Like RuPaul's Drag Race on Facebook: https://www.facebook.com/rupaulsdragrace Follow RuPaul's Drag Race on Instagram: https://www.instagram.com/rupaulsdragrace/ Follow RuPaul's Drag Race on Twitter: https://twitter.com/rupaulsdragrace
published: 09 Aug 2018 -
Category Meaning
Video shows what category means. A group, often named or numbered, to which items are assigned based on similarity or defined criteria.. A collection of objects, together with a transitively closed collection of composable arrows between them, such that every object has an identity arrow, and such that arrow composition is associative.. category synonyms: Wikisaurus:class, class, family, genus, group, kingdom, order, phylum, race, tribe, type. category pronunciation. How to pronounce, definition by Wiktionary dictionary. category meaning. Powered by MaryTTS
published: 15 Apr 2015 -
Universal Construction | Category Theory and Why We Care 1.2
To fully utilise the exciting category theory we've learnt so far, we need a way to abstract definitions from a specific category and then be able to apply them in any category we want. The solution to this is universal construction. This video will explore the process of universal construction and see it used in practice, which will further expose some elegant relationships between categories that we've seen before. Taking examples from mathematical proofs, functional programming and beyond, this is the next major step into abstraction that our category theory journey takes us. ― Timestamps ― 0:00 - Intro 1:03 - Isomorphism 5:22 - Terminal object 10:41 - Universal construction 12:27 - Conjunction 17:32 - Product 18:29 - Pair type 24:12 - Outro 25:00 - Exercise ― Credits ― All animati...
published: 03 Dec 2024 -
ONE N’ ONLY／“Category” Music Video
【ファンクラブツアー】 ONE N’ ONLY FC TOUR 2024 ～SWAG祭～ 2024.8.22(木)大阪：Zepp Namba (OSAKA) 2024.8.23(金)愛知：Zepp Nagoya 2024.8.26(月)-27(火)東京：Zepp Haneda (TOKYO) https://one-n-only.jp/live/live30214/ 【グループ史上最大規模のツアー】 ONE N’ SWAG 2024 ¿Fiesta? 2024.9.27(金)-28(土)東京：東京国際フォーラム ホールC 2024.10.14(月祝)愛知：Niterra日本特殊陶業市民会館 フォレストホール 2024.11.15(金)大阪：大阪国際会議場(グランキューブ大阪) 2024年11月15日(金) 開場17:30／開演18:30 2025.1.18(土)東京：東京ガーデンシアター https://one-n-only.jp/live/live30130/ 【New Release!!】 3rd EP「Fiesta」 https://one-n-only.jp/news/news30371/ 2024.4.10（wed） ONE N’ ONLY ／ DOMINO https://ssm.lnk.to/DOMINO_ONO 2024.3.1（fri） ONE N’ ONLY ／ TALKIN' https://ssm.lnk.to/TALKIN ----------------------------------------------------------------------------------------------------------------------------------------- スターダストプロモーション所属の6人組の男性グ...
published: 23 Aug 2019 -
Category is: PRECISION 💂✨
Follow us on: TikTok: https://www.tiktok.com/@rockettes Instagram: https://www.instagram.com/therockettes Facebook: https://www.facebook.com/rockettes/ Twitter: https://twitter.com/Rockettes Threads: https://www.threads.net/@therockettes Visit our website for the latest from the kickline: https://www.rockettes.com/ #Rockettes #Shorts #Kickline
published: 27 Oct 2024 -
Category Theory 1.1: Motivation and Philosophy
Motivation and philosophy
published: 25 Aug 2016 -
Lil Durk & Tee Grizzley "Category Hoes" (Official Audio)
Listen to the official audio of "Category Hoes" by Lil Durk & Tee Grizzley. Subscribe to Lil Durk's official channel for exclusive music videos and behind the scenes looks: http://bit.ly/Subscribe-to-Durk More Lil Durk: https://fb.com/lildurk https://twitter.com/lildurk_ https://instagram.com/Imlildurk2x http://officiallildurk.com
published: 08 Dec 2017 -
Won in wedding cake category ✨✨
Won in wedding cake category ✨✨ Overjoyed to announce that I won in the Wedding Cake Category at the India Bake Show 2024, held in Bengaluru! It’s been an incredible journey perfecting every detail, and this recognition means the world to me. Thank you to everyone who has believed in me and my work—your support makes every win even more special!” #cakesandbakeschool #shortsvideo #ytshorts #weddingcake
published: 17 Dec 2024 -
Category is.....animals! 🐈 🐇 🐄
#animal #categories #head2head #breadbasket
published: 14 Sep 2024
developed with YouTube
26:20
A Sensible Introduction to Category Theory
- Order: Reorder
- Duration: 26:20
- Uploaded Date: 22 Jun 2022
- views: 449007
Remember when I used a video with a coconut in the thumbnail to drive a stake through the heart of mathematical structure? Today, in this introduction to the ba...
Remember when I used a video with a coconut in the thumbnail to drive a stake through the heart of mathematical structure? Today, in this introduction to the basics of category theory, I attempt to remove it.
27 Unhelpful Facts About Category Theory: https://www.youtube.com/watch?v=H0Ek86IH-3Y
MetaMaths on category theory: https://www.youtube.com/watch?v=ZG6t0-JMrw0
My dissertation on the equivalence between the category of monoidal categories and the category of representable multicategories: https://drive.google.com/file/d/1hAkV1qSnUutzQMMQi48yo_fXsgb1YnbL/view?usp=sharing
FURTHER READING
Basic Category Theory (Tom Leinster): https://arxiv.org/pdf/1612.09375.pdf
Categories for the Working Mathematician (Saunders Mac Lane): http://www.mtm.ufsc.br/~ebatista/2016-2/maclanecat.pdf
Category Theory for Computing Science (Michael Barr and Charles Wells): https://www.math.mcgill.ca/triples/Barr-Wells-ctcs.pdf
Category Theory for the Sciences (David Spivak): https://math.mit.edu/~dspivak/CT4S.pdf
Bartosz Milewski on category theory: https://www.youtube.com/watch?v=I8LbkfSSR58&list=PLbgaMIhjbmEnaH_LTkxLI7FMa2HsnawM_
Emily Riehl on category theory: https://www.youtube.com/watch?v=WLkMBMUk48E
MUSIC
Meditation Aquatic
369 (Epidemic Sound)
Nights Full of Overthinking
Lionel Quick (Epidemic Sound)
Oregano
Vendla (Epidemic Sound)
Wash
Timothy Infinite (Epidemic Sound)
Wind
Osoku (Epidemic Sound)
https://wn.com/A_Sensible_Introduction_To_Category_Theory
Remember when I used a video with a coconut in the thumbnail to drive a stake through the heart of mathematical structure? Today, in this introduction to the basics of category theory, I attempt to remove it.
27 Unhelpful Facts About Category Theory: https://www.youtube.com/watch?v=H0Ek86IH-3Y
MetaMaths on category theory: https://www.youtube.com/watch?v=ZG6t0-JMrw0
My dissertation on the equivalence between the category of monoidal categories and the category of representable multicategories: https://drive.google.com/file/d/1hAkV1qSnUutzQMMQi48yo_fXsgb1YnbL/view?usp=sharing
FURTHER READING
Basic Category Theory (Tom Leinster): https://arxiv.org/pdf/1612.09375.pdf
Categories for the Working Mathematician (Saunders Mac Lane): http://www.mtm.ufsc.br/~ebatista/2016-2/maclanecat.pdf
Category Theory for Computing Science (Michael Barr and Charles Wells): https://www.math.mcgill.ca/triples/Barr-Wells-ctcs.pdf
Category Theory for the Sciences (David Spivak): https://math.mit.edu/~dspivak/CT4S.pdf
Bartosz Milewski on category theory: https://www.youtube.com/watch?v=I8LbkfSSR58&list=PLbgaMIhjbmEnaH_LTkxLI7FMa2HsnawM_
Emily Riehl on category theory: https://www.youtube.com/watch?v=WLkMBMUk48E
MUSIC
Meditation Aquatic
369 (Epidemic Sound)
Nights Full of Overthinking
Lionel Quick (Epidemic Sound)
Oregano
Vendla (Epidemic Sound)
Wash
Timothy Infinite (Epidemic Sound)
Wind
Osoku (Epidemic Sound)
- published: 22 Jun 2022
- views: 449007
3:16
'Category Is...' Performance w/ Peppermint, Sasha, Trinity & Shea 👯♀️ | RuPaul's Drag Race Season 9
- Order: Reorder
- Duration: 3:16
- Uploaded Date: 09 Aug 2018
- views: 14254884
Start the music and gag over Peppermint, Sasha Velour, Trinity Taylor, and Shea Coulee during the 'Category Is' Challenge on RuPaul’s Drag Race Season 9.
#VH1...
Start the music and gag over Peppermint, Sasha Velour, Trinity Taylor, and Shea Coulee during the 'Category Is' Challenge on RuPaul’s Drag Race Season 9.
#VH1 #DragRace
More from RuPaul's Drag Race:
Official Website: http://www.vh1.com/shows/rupauls-drag-race
Like RuPaul's Drag Race on Facebook: https://www.facebook.com/rupaulsdragrace
Follow RuPaul's Drag Race on Instagram: https://www.instagram.com/rupaulsdragrace/
Follow RuPaul's Drag Race on Twitter: https://twitter.com/rupaulsdragrace
https://wn.com/'Category_Is...'_Performance_W_Peppermint,_Sasha,_Trinity_Shea_👯♀️_|_Rupaul's_Drag_Race_Season_9
Start the music and gag over Peppermint, Sasha Velour, Trinity Taylor, and Shea Coulee during the 'Category Is' Challenge on RuPaul’s Drag Race Season 9.
#VH1 #DragRace
More from RuPaul's Drag Race:
Official Website: http://www.vh1.com/shows/rupauls-drag-race
Like RuPaul's Drag Race on Facebook: https://www.facebook.com/rupaulsdragrace
Follow RuPaul's Drag Race on Instagram: https://www.instagram.com/rupaulsdragrace/
Follow RuPaul's Drag Race on Twitter: https://twitter.com/rupaulsdragrace
- published: 09 Aug 2018
- views: 14254884
0:53
Category Meaning
- Order: Reorder
- Duration: 0:53
- Uploaded Date: 15 Apr 2015
- views: 76770
Video shows what category means. A group, often named or numbered, to which items are assigned based on similarity or defined criteria.. A collection of objects...
Video shows what category means. A group, often named or numbered, to which items are assigned based on similarity or defined criteria.. A collection of objects, together with a transitively closed collection of composable arrows between them, such that every object has an identity arrow, and such that arrow composition is associative.. category synonyms: Wikisaurus:class, class, family, genus, group, kingdom, order, phylum, race, tribe, type. category pronunciation. How to pronounce, definition by Wiktionary dictionary. category meaning. Powered by MaryTTS
https://wn.com/Category_Meaning
Video shows what category means. A group, often named or numbered, to which items are assigned based on similarity or defined criteria.. A collection of objects, together with a transitively closed collection of composable arrows between them, such that every object has an identity arrow, and such that arrow composition is associative.. category synonyms: Wikisaurus:class, class, family, genus, group, kingdom, order, phylum, race, tribe, type. category pronunciation. How to pronounce, definition by Wiktionary dictionary. category meaning. Powered by MaryTTS
- published: 15 Apr 2015
- views: 76770
25:50
Universal Construction | Category Theory and Why We Care 1.2
- Order: Reorder
- Duration: 25:50
- Uploaded Date: 03 Dec 2024
- views: 23955
To fully utilise the exciting category theory we've learnt so far, we need a way to abstract definitions from a specific category and then be able to apply them...
To fully utilise the exciting category theory we've learnt so far, we need a way to abstract definitions from a specific category and then be able to apply them in any category we want. The solution to this is universal construction.
This video will explore the process of universal construction and see it used in practice, which will further expose some elegant relationships between categories that we've seen before. Taking examples from mathematical proofs, functional programming and beyond, this is the next major step into abstraction that our category theory journey takes us.
― Timestamps ―
0:00 - Intro
1:03 - Isomorphism
5:22 - Terminal object
10:41 - Universal construction
12:27 - Conjunction
17:32 - Product
18:29 - Pair type
24:12 - Outro
25:00 - Exercise
― Credits ―
All animation and voiceover created by Eyesomorphic.
Background music: 'Sonder', composed by Caleb Peppiatt.
― Further Reading ―
Category Theory and Why We Care, by Eyesomorphic (Lecture series): https://youtube.com/playlist?list=PLoCKNPo3VR0I2wqT2wemCNIlpjdy_Ry_q&si=9UOLXRFqNdfgGXlI
Algebra: Chapter 0 (Book), by Paulo Aluffi
https://wn.com/Universal_Construction_|_Category_Theory_And_Why_We_Care_1.2
To fully utilise the exciting category theory we've learnt so far, we need a way to abstract definitions from a specific category and then be able to apply them in any category we want. The solution to this is universal construction.
This video will explore the process of universal construction and see it used in practice, which will further expose some elegant relationships between categories that we've seen before. Taking examples from mathematical proofs, functional programming and beyond, this is the next major step into abstraction that our category theory journey takes us.
― Timestamps ―
0:00 - Intro
1:03 - Isomorphism
5:22 - Terminal object
10:41 - Universal construction
12:27 - Conjunction
17:32 - Product
18:29 - Pair type
24:12 - Outro
25:00 - Exercise
― Credits ―
All animation and voiceover created by Eyesomorphic.
Background music: 'Sonder', composed by Caleb Peppiatt.
― Further Reading ―
Category Theory and Why We Care, by Eyesomorphic (Lecture series): https://youtube.com/playlist?list=PLoCKNPo3VR0I2wqT2wemCNIlpjdy_Ry_q&si=9UOLXRFqNdfgGXlI
Algebra: Chapter 0 (Book), by Paulo Aluffi
- published: 03 Dec 2024
- views: 23955
4:13
ONE N’ ONLY／“Category” Music Video
- Order: Reorder
- Duration: 4:13
- Uploaded Date: 23 Aug 2019
- views: 3916980
【ファンクラブツアー】
ONE N’ ONLY FC TOUR 2024 ～SWAG祭～
2024.8.22(木)大阪：Zepp Namba (OSAKA)
2024.8.23(金)愛知：Zepp Nagoya
2024.8.26(月)-27(火)東京：Zepp Haneda (TOKYO)
https://one-n...
【ファンクラブツアー】
ONE N’ ONLY FC TOUR 2024 ～SWAG祭～
2024.8.22(木)大阪：Zepp Namba (OSAKA)
2024.8.23(金)愛知：Zepp Nagoya
2024.8.26(月)-27(火)東京：Zepp Haneda (TOKYO)
https://one-n-only.jp/live/live30214/
【グループ史上最大規模のツアー】
ONE N’ SWAG 2024 ¿Fiesta?
2024.9.27(金)-28(土)東京：東京国際フォーラム ホールC
2024.10.14(月祝)愛知：Niterra日本特殊陶業市民会館 フォレストホール
2024.11.15(金)大阪：大阪国際会議場(グランキューブ大阪)
2024年11月15日(金) 開場17:30／開演18:30
2025.1.18(土)東京：東京ガーデンシアター
https://one-n-only.jp/live/live30130/
【New Release!!】
3rd EP「Fiesta」
https://one-n-only.jp/news/news30371/
2024.4.10（wed）
ONE N’ ONLY ／ DOMINO
https://ssm.lnk.to/DOMINO_ONO
2024.3.1（fri）
ONE N’ ONLY ／ TALKIN'
https://ssm.lnk.to/TALKIN
-----------------------------------------------------------------------------------------------------------------------------------------
スターダストプロモーション所属の6人組の男性グループ。
ボーカルTETTA（1997年11月24日生まれ）、REI（1997年1月2日生まれ）、EIKU（1999年12月19日生まれ）。ラップ&ダンサーHAYATO（1999年9月17日生まれ）、KENSHIN（1999年7月8日生まれ）、NAOYA（1998年4月6日生まれ）からなる6人組。デビュー以来"JK-POP"という独自のスタイルで活動していき、2023年の南米ワンマンツアーを経て、Latin カルチャーを取り込み"JK-Pop"と"Latin Music"を融合した、さらなる独自のスタイル"Jatin Pop"へと進化し、唯一無二のスタイルを貫き続けるダンス&ボーカルグループ。
Music Videoは世界各国注目され、南米・アジア圏・欧州からのアクセスが殺到し、合計再生回数は3000万回を突破！TikTokフォロワー数は、日本人男性音楽アーティストでは1位となる580万人超え! 動画の総再生回数は6.2億回を突破!!
2022年7月にはブラジルで開催された南米最大のアニメフェス『Anime Friends 2022』で初の海外パフォーマンスを成功させ、2023年4月にはワンマンでのラテンアメリカツアー「LATIN TOUR 2023」を開催した。
2023年10月より47都道府県ツアー『ONE N’ SWAG ～Hook Up!!!!!!～』を開催。ツアーファイナルとなるパシフィコ横浜公演を含む全47公演がソールドアウトした。
ONE N’ ONLY is a six-piece boy band comprised of TETTA, REI, EIKU, HAYATO, KENSHIN, and NAOYA. Formed by renown Japanese talent agency Stardust Promotion, the members were originally from two separate bands, EBiSSH and SBC (Satori Boys Club).
Since their debut in 2018, they’ve boasted their unique ability to blend genres, starting with JK-POP. They have since evolved to Jatin Pop, a blend of Japanese and Latin pop, after finding international TikTok success.
The band’s music videos have garnered views from Asia, Latin and North America, and Europe, with a total view count exceeding 30 million. They are Japan’s Number 1 most followed male musical artist on TikTok with over 5.8 million followers and 620 million views.
In 2022, the band performed overseas for the first time at South America’s largest Anime event, Anime Friends 2022. In the following year, they embarked on their headlining LATIN TOUR 2023. Later in 2023, the band toured across all 47 of Japan’s prefectures, closing their tour with a sold-out show at Pacifico Yokohama.
-----------------------------------------------------------------------------------------------------------------------------------------
#ワンエン #ONENONLY #ONO #ワンエンTV
https://wn.com/One_N’_Only／“Category”_Music_Video
【ファンクラブツアー】
ONE N’ ONLY FC TOUR 2024 ～SWAG祭～
2024.8.22(木)大阪：Zepp Namba (OSAKA)
2024.8.23(金)愛知：Zepp Nagoya
2024.8.26(月)-27(火)東京：Zepp Haneda (TOKYO)
https://one-n-only.jp/live/live30214/
【グループ史上最大規模のツアー】
ONE N’ SWAG 2024 ¿Fiesta?
2024.9.27(金)-28(土)東京：東京国際フォーラム ホールC
2024.10.14(月祝)愛知：Niterra日本特殊陶業市民会館 フォレストホール
2024.11.15(金)大阪：大阪国際会議場(グランキューブ大阪)
2024年11月15日(金) 開場17:30／開演18:30
2025.1.18(土)東京：東京ガーデンシアター
https://one-n-only.jp/live/live30130/
【New Release!!】
3rd EP「Fiesta」
https://one-n-only.jp/news/news30371/
2024.4.10（wed）
ONE N’ ONLY ／ DOMINO
https://ssm.lnk.to/DOMINO_ONO
2024.3.1（fri）
ONE N’ ONLY ／ TALKIN'
https://ssm.lnk.to/TALKIN
-----------------------------------------------------------------------------------------------------------------------------------------
スターダストプロモーション所属の6人組の男性グループ。
ボーカルTETTA（1997年11月24日生まれ）、REI（1997年1月2日生まれ）、EIKU（1999年12月19日生まれ）。ラップ&ダンサーHAYATO（1999年9月17日生まれ）、KENSHIN（1999年7月8日生まれ）、NAOYA（1998年4月6日生まれ）からなる6人組。デビュー以来"JK-POP"という独自のスタイルで活動していき、2023年の南米ワンマンツアーを経て、Latin カルチャーを取り込み"JK-Pop"と"Latin Music"を融合した、さらなる独自のスタイル"Jatin Pop"へと進化し、唯一無二のスタイルを貫き続けるダンス&ボーカルグループ。
Music Videoは世界各国注目され、南米・アジア圏・欧州からのアクセスが殺到し、合計再生回数は3000万回を突破！TikTokフォロワー数は、日本人男性音楽アーティストでは1位となる580万人超え! 動画の総再生回数は6.2億回を突破!!
2022年7月にはブラジルで開催された南米最大のアニメフェス『Anime Friends 2022』で初の海外パフォーマンスを成功させ、2023年4月にはワンマンでのラテンアメリカツアー「LATIN TOUR 2023」を開催した。
2023年10月より47都道府県ツアー『ONE N’ SWAG ～Hook Up!!!!!!～』を開催。ツアーファイナルとなるパシフィコ横浜公演を含む全47公演がソールドアウトした。
ONE N’ ONLY is a six-piece boy band comprised of TETTA, REI, EIKU, HAYATO, KENSHIN, and NAOYA. Formed by renown Japanese talent agency Stardust Promotion, the members were originally from two separate bands, EBiSSH and SBC (Satori Boys Club).
Since their debut in 2018, they’ve boasted their unique ability to blend genres, starting with JK-POP. They have since evolved to Jatin Pop, a blend of Japanese and Latin pop, after finding international TikTok success.
The band’s music videos have garnered views from Asia, Latin and North America, and Europe, with a total view count exceeding 30 million. They are Japan’s Number 1 most followed male musical artist on TikTok with over 5.8 million followers and 620 million views.
In 2022, the band performed overseas for the first time at South America’s largest Anime event, Anime Friends 2022. In the following year, they embarked on their headlining LATIN TOUR 2023. Later in 2023, the band toured across all 47 of Japan’s prefectures, closing their tour with a sold-out show at Pacifico Yokohama.
-----------------------------------------------------------------------------------------------------------------------------------------
#ワンエン #ONENONLY #ONO #ワンエンTV
- published: 23 Aug 2019
- views: 3916980
0:16
Category is: PRECISION 💂✨
- Order: Reorder
- Duration: 0:16
- Uploaded Date: 27 Oct 2024
- views: 2455808
Follow us on:
TikTok: https://www.tiktok.com/@rockettes
Instagram: https://www.instagram.com/therockettes
Facebook: https://www.facebook.com/rockettes/
Twitter:...
Follow us on:
TikTok: https://www.tiktok.com/@rockettes
Instagram: https://www.instagram.com/therockettes
Facebook: https://www.facebook.com/rockettes/
Twitter: https://twitter.com/Rockettes
Threads: https://www.threads.net/@therockettes
Visit our website for the latest from the kickline: https://www.rockettes.com/
#Rockettes #Shorts #Kickline
https://wn.com/Category_Is_Precision_💂✨
Follow us on:
TikTok: https://www.tiktok.com/@rockettes
Instagram: https://www.instagram.com/therockettes
Facebook: https://www.facebook.com/rockettes/
Twitter: https://twitter.com/Rockettes
Threads: https://www.threads.net/@therockettes
Visit our website for the latest from the kickline: https://www.rockettes.com/
#Rockettes #Shorts #Kickline
- published: 27 Oct 2024
- views: 2455808
46:46
Category Theory 1.1: Motivation and Philosophy
- Order: Reorder
- Duration: 46:46
- Uploaded Date: 25 Aug 2016
- views: 348092
Motivation and philosophy
Motivation and philosophy
https://wn.com/Category_Theory_1.1_Motivation_And_Philosophy
Motivation and philosophy
- published: 25 Aug 2016
- views: 348092
3:26
Lil Durk & Tee Grizzley "Category Hoes" (Official Audio)
- Order: Reorder
- Duration: 3:26
- Uploaded Date: 08 Dec 2017
- views: 905153
Listen to the official audio of "Category Hoes" by Lil Durk & Tee Grizzley.
Subscribe to Lil Durk's official channel for exclusive music videos and behind the ...
Listen to the official audio of "Category Hoes" by Lil Durk & Tee Grizzley.
Subscribe to Lil Durk's official channel for exclusive music videos and behind the scenes looks: http://bit.ly/Subscribe-to-Durk
More Lil Durk:
https://fb.com/lildurk
https://twitter.com/lildurk_
https://instagram.com/Imlildurk2x
http://officiallildurk.com
https://wn.com/Lil_Durk_Tee_Grizzley_Category_Hoes_(Official_Audio)
Listen to the official audio of "Category Hoes" by Lil Durk & Tee Grizzley.
Subscribe to Lil Durk's official channel for exclusive music videos and behind the scenes looks: http://bit.ly/Subscribe-to-Durk
More Lil Durk:
https://fb.com/lildurk
https://twitter.com/lildurk_
https://instagram.com/Imlildurk2x
http://officiallildurk.com
- published: 08 Dec 2017
- views: 905153
0:48
Won in wedding cake category ✨✨
- Order: Reorder
- Duration: 0:48
- Uploaded Date: 17 Dec 2024
- views: 245
Won in wedding cake category ✨✨
Overjoyed to announce that I won in the Wedding Cake Category at the India Bake Show 2024, held in Bengaluru! It’s been an incr...
Won in wedding cake category ✨✨
Overjoyed to announce that I won in the Wedding Cake Category at the India Bake Show 2024, held in Bengaluru! It’s been an incredible journey perfecting every detail, and this recognition means the world to me. Thank you to everyone who has believed in me and my work—your support makes every win even more special!”
#cakesandbakeschool #shortsvideo #ytshorts #weddingcake
https://wn.com/Won_In_Wedding_Cake_Category_✨✨
Won in wedding cake category ✨✨
Overjoyed to announce that I won in the Wedding Cake Category at the India Bake Show 2024, held in Bengaluru! It’s been an incredible journey perfecting every detail, and this recognition means the world to me. Thank you to everyone who has believed in me and my work—your support makes every win even more special!”
#cakesandbakeschool #shortsvideo #ytshorts #weddingcake
- published: 17 Dec 2024
- views: 245
0:19
Category is.....animals! 🐈 🐇 🐄
- Order: Reorder
- Duration: 0:19
- Uploaded Date: 14 Sep 2024
- views: 152046
#animal #categories #head2head #breadbasket
#animal #categories #head2head #breadbasket
https://wn.com/Category_Is.....Animals_🐈_🐇_🐄
#animal #categories #head2head #breadbasket
- published: 14 Sep 2024
- views: 152046
56:34
What is Category Theory in mathematics? Johns Hopkins' Dr. Emily Riehl explains
The President's Frontier Award was established with a $2.5 million donation from trustee L...
published: 16 Dec 2020
What is Category Theory in mathematics? Johns Hopkins' Dr. Emily Riehl explains
What is Category Theory in mathematics? Johns Hopkins' Dr. Emily Riehl explains
- Report rights infringement
- published: 16 Dec 2020
- views: 40642
The President's Frontier Award was established with a $2.5 million donation from trustee Louis J. Forster. Forster helped design the award to support exceptional scholars among the Johns Hopkins faculty who are on the cusp of transforming their fields. The award recognizes one person each year with $250,000 in funding for their work.
This PFA lecture features 2020 recipient Dr. Emily Riehl presenting on Category Theory. Thinking categorically can help serve as a guide post as you trek the grand scheme of (mathematical) things. As written in Quanta Magazine in a 2020 interview with Riehl, “category theory and its next-generation version, higher category theory, are central to many fields of math, from algebraic geometry to mathematical physics. In those areas, Riehl said, ‘I think it would be impossible to describe the kind of basic objects of study without categorical language.’”
Join us for this fantastic event honoring the brilliant work of Dr. Riehl, opened by Provost Sunil Kumar and Dr. John Toscano. Denis Wirtz, Vice Provost for Research, provides closing remarks. To learn more, visit jhu.edu/hopkinsathome
11:06
The Map of Mathematics
The entire field of mathematics summarised in a single map! This shows how pure mathematic...
published: 01 Feb 2017
The Map of Mathematics
The Map of Mathematics
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- published: 01 Feb 2017
- views: 14122400
The entire field of mathematics summarised in a single map! This shows how pure mathematics and applied mathematics relate to each other and all of the sub-topics they are made from.
#mathematics #DomainOfScience
If you would like to buy a poster of this map, they are available here:
North America: https://store.dftba.com/products/map-of-mathematics-poster
Everywhere else: http://www.redbubble.com/people/dominicwalliman/works/25095968-the-map-of-mathematics
French version: https://www.redbubble.com/people/dominicwalliman/works/40572671-the-map-of-mathematics-french-version?asc=u
Spanish Version: https://www.redbubble.com/people/dominicwalliman/works/40572693-the-map-of-mathematics-spanish-version?asc=u
I have also made a version available for educational use which you can find here: https://www.flickr.com/photos/95869671@N08/32264483720/in/dateposted-public/
To err is to human, and I human a lot. I always try my best to be as correct as possible, but unfortunately I make mistakes. This is the errata where I correct my silly mistakes. My goal is to one day do a video with no errors!
1. The number one is not a prime number. The definition of a prime number is a number can be divided evenly only by 1, or itself. And it must be a whole number GREATER than 1. (This last bit is the bit I forgot).
2. In the trigonometry section I drew cos(theta) = opposite / adjacent. This is the kind of thing you learn in high school and guess what. I got it wrong! Dummy. It should be cos(theta) = adjacent / hypotenuse.
3. My drawing of dice is slightly wrong. Most dice have their opposite sides adding up to 7, so when I drew 3 and 4 next to each other that is incorrect.
4. I said that the Gödel Incompleteness Theorems implied that mathematics is made up by humans, but that is wrong, just ignore that statement. I have learned more about it now, here is a good video explaining it: https://youtu.be/O4ndIDcDSGc
5. In the animation about imaginary numbers I drew the real axis as vertical and the imaginary axis as horizontal which is opposite to the conventional way it is done.
Thanks so much to my supporters on Patreon. I hope to make money from my videos one day, but I’m not there yet! If you enjoy my videos and would like to help me make more this is the best way and I appreciate it very much. https://www.patreon.com/domainofscience
Here are links to some of the sources I used in this video.
Links:
Summary of mathematics: https://en.wikipedia.org/wiki/Mathematics
Earliest human counting: http://mathtimeline.weebly.com/early-human-counting-tools.html
First use of zero: https://en.wikipedia.org/wiki/0#History http://www.livescience.com/27853-who-invented-zero.html
First use of negative numbers: https://www.quora.com/Who-is-the-inventor-of-negative-numbers
Renaissance science: https://en.wikipedia.org/wiki/History_of_science_in_the_Renaissance
History of complex numbers: http://rossroessler.tripod.com/ https://en.wikipedia.org/wiki/Mathematics
Proof that pi is irrational: https://www.quora.com/How-do-you-prove-that-pi-is-an-irrational-number
and https://en.wikipedia.org/wiki/Proof_that_%CF%80_is_irrational#Laczkovich.27s_proof
Also, if you enjoyed this video, you will probably like my science books, available in all good books shops around the work and is printed in 16 languages. Links are below or just search for Professor Astro Cat. They are fun children's books aimed at the age range 7-12. But they are also a hit with adults who want good explanations of science. The books have won awards and the app won a Webby.
Frontiers of Space: http://nobrow.net/shop/professor-astro-cats-frontiers-of-space/
Atomic Adventure: http://nobrow.net/shop/professor-astro-cats-atomic-adventure/
Intergalactic Activity Book: http://nobrow.net/shop/professor-astro-cats-intergalactic-activity-book/
Solar System App: http://www.minilabstudios.com/apps/professor-astro-cats-solar-system/
Find me on twitter, instagram, and my website:
http://dominicwalliman.com
https://twitter.com/DominicWalliman
https://www.instagram.com/dominicwalliman
https://www.facebook.com/dominicwalliman
57:56
Category Theory For Beginners: Introduction
Category theory is close to the perfect language. It can be used to describe many mathemat...
published: 13 May 2019
Category Theory For Beginners: Introduction
Category Theory For Beginners: Introduction
- Report rights infringement
- published: 13 May 2019
- views: 90436
Category theory is close to the perfect language. It can be used to describe many mathematical ideas, and see the relations between them, and their deeper structure. This is the first video in a course where we will carefully introduce the main ideas of category theory, and motivate them with lots of applications. This first video gives the definition of a category and give some motivation for studying the subject. In particular we define a category, give the definition of a monoid, we define a pre-ordered set (preorder), we define the category Set, of sets and functions. We introduce functional programming. We define the final object (terminal object), and explain how the ideas can be used to do set theory without considering the elements within sets directly.
Some people have said they want to support my efforts to make educational videos and software, and so I have made a Patreon page
https://www.patreon.com/richardsouthwell
Any support would really help me produce more videos and software.
2:47
What is Category (mathematics)?, Explain Category (mathematics), Define Category (mathematics)
~~~ Category (mathematics) ~~~
Title: What is Category (mathematics)?, Explain Category (...
published: 11 Jul 2018
What is Category (mathematics)?, Explain Category (mathematics), Define Category (mathematics)
What is Category (mathematics)?, Explain Category (mathematics), Define Category (mathematics)
- Report rights infringement
- published: 11 Jul 2018
- views: 1813
~~~ Category (mathematics) ~~~
Title: What is Category (mathematics)?, Explain Category (mathematics), Define Category (mathematics)
Created on: 2018-07-11
Source Link: https://en.wikipedia.org/wiki/Category_(mathematics)
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Description: In mathematics, a category is an algebraic structure similar to a group but without requiring inverse or closure properties. It comprises "objects" that are linked by "arrows". A category has two basic properties: the ability to compose the arrows associatively and the existence of an identity arrow for each object. A simple example is the category of sets, whose objects are sets and whose arrows are functions. Category theory is a branch of mathematics that seeks to generalize all of mathematics in terms of categories, independent of what their objects and arrows represent. Virtually every branch of modern mathematics can be described in terms of categories, and doing so often reveals deep insights and similarities between seemingly different areas of mathematics. As such, category theory provides an alternative foundation for mathematics to set theory and other proposed axiomatic foundations. In general, the objects and arrows may be abstract entities of any kind, and the notion of category provides a fundamental and abstract way to describe mathematical entities and their relationships. In addition to formalizing mathematics, category theory is also used to formalize many other systems in computer science, such as the semantics of programming languages. Two categories are the same if they have the same collection of objects, the same collection of arrows, and the same associative method of composing any pair of arrows. Two different categories may also be considered "equivalent" for purposes of category theory, even if they do not have precisely the same structure. Well-known categories are denoted by a short capitalized word or abbreviation in bold or italics: examples include Set, the category of sets and set functions; Ring, the category of rings and ring homomorphisms; and Top, the category of topological spaces and continuous maps. All of the preceding categories have the identity map as identity arrow and composition as the associative operation on arrows. The classic and still much used text on category theory is Categories for the Working Mathematician by Saunders Mac Lane. Other references are given in the References below. The basic definitions in this article are contained within the first few chapters of any of these books. Any monoid can be understood as a special sort of category , and so can any preorder.
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To see your favorite topic here, fill out this request form: https://docs.google.com/forms/d/e/1FAIpQLScU0dLbeWsc01IC0AaO8sgaSgxMFtvBL31c_pjnwEZUiq99Fw/viewform
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Source: Wikipedia.org articles, adapted under https://creativecommons.org/licenses/by-sa/3.0/ license.
Support: Donations can be made from https://wikimediafoundation.org/wiki/Ways_to_Give to support Wikimedia Foundation and knowledge sharing.
55:10
Category Theory: Visual Mathematics for the 21st century
RCON 3 Day 3 track 4 Session 4
Category Theory: Visual Mathematics for the 21st century by...
published: 14 Sep 2018
Category Theory: Visual Mathematics for the 21st century
Category Theory: Visual Mathematics for the 21st century
- Report rights infringement
- published: 14 Sep 2018
- views: 1704
RCON 3 Day 3 track 4 Session 4
Category Theory: Visual Mathematics for the 21st century by Jamie Vicary
1:09:46
ACT@UCR Seminar: Mathematics in the 21st Century - John Baez
The global warming crisis is part of a bigger transformation in which humanity realizes th...
published: 13 Jan 2019
ACT@UCR Seminar: Mathematics in the 21st Century - John Baez
ACT@UCR Seminar: Mathematics in the 21st Century - John Baez
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- published: 13 Jan 2019
- views: 3767
The global warming crisis is part of a bigger transformation in which humanity realizes that the Earth is a finite system and that our population, energy usage, and the like cannot continue to grow exponentially. If civilization survives this transformation, it will affect mathematics – and be affected by it – just as dramatically as the agricultural revolution or industrial revolution. We should get ready!
slides: http://math.ucr.edu/home/baez/planet/planet_ucr.pdf
This talk is part of the Applied Category Theory at U. C. Riverside Seminar: : https://johncarlosbaez.wordpress.com/2018/12/14/applied-category-theory-seminar/
Edited by Paola Fernandez
1:16:51
Emily Riehl on Topology, Categories, and the Future of Mathematics
Patreon: https://www.patreon.com/seanmcarroll
Blog post with audio player, show notes, and...
published: 10 May 2021
Emily Riehl on Topology, Categories, and the Future of Mathematics
Emily Riehl on Topology, Categories, and the Future of Mathematics
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- published: 10 May 2021
- views: 21094
Patreon: https://www.patreon.com/seanmcarroll
Blog post with audio player, show notes, and transcript: https://www.preposterousuniverse.com/podcast/2021/05/10/146-emily-riehl-on-topology-categories-and-the-future-of-mathematics/
“A way that math can make the world a better place is by making it a more interesting place to be a conscious being.” So says mathematician Emily Riehl near the start of this episode, and it’s a good summary of what’s to come. Emily works in realms of topology and category theory that are far away from practical applications, or even to some non-practical areas of theoretical physics. But they help us think about what is possible and how everything fits together, and what’s more interesting than that? We talk about what topology is, the specific example of homotopy — how things deform into other things — and how thinking about that leads us into groups, rings, groupoids, and ultimately to category theory, the most abstract of them all.
Emily Riehl received a Ph.D in mathematics from the University of Chicago. She is currently an associate professor of mathematics at Johns Hopkins University. Among her honors are the JHU President’s Frontier Award and the Joan & Joseph Birman Research Prize. She is author of Categorical Homotopy Theory, and co-author of the upcoming Elements of ∞-Category Theory. She competed on the United States women’s national Australian rules football team, where she served as vice-captain.
Mindscape Podcast playlist: https://www.youtube.com/playlist?list=PLrxfgDEc2NxY_fRExpDXr87tzRbPCaA5x
#podcast #ideas #science #philosophy #culture
11:45
Category (mathematics)
If you find our videos helpful you can support us by buying something from amazon.
https:/...
published: 22 Jan 2016
Category (mathematics)
Category (mathematics)
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- published: 22 Jan 2016
- views: 519
If you find our videos helpful you can support us by buying something from amazon.
https://www.amazon.com/?tag=wiki-audio-20
Category (mathematics)
In mathematics, a category is an algebraic structure that comprises "objects" that are linked by "arrows".A category has two basic properties: the ability to compose the arrows associatively and the existence of an identity arrow for each object.
=======Image-Copyright-Info========
License: Creative Commons Attribution-Share Alike 4.0 (CC BY-SA 4.0)
LicenseLink: http://creativecommons.org/licenses/by-sa/4.0
Author-Info: IkamusumeFan
Image Source: https://en.wikipedia.org/wiki/File:Category_SVG.svg
=======Image-Copyright-Info========
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https://www.youtube.com/watch?v=kafQy7Xk4IQ
7:13
Classification/ branches of mathematics | Application | Useful maths | Learning | Mathsfun
Hello everyone!!
Iss video me classification/ branches of maths ke baare me discuss kiya ...
published: 25 May 2020
Classification/ branches of mathematics | Application | Useful maths | Learning | Mathsfun
Classification/ branches of mathematics | Application | Useful maths | Learning | Mathsfun
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- published: 25 May 2020
- views: 35952
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Category (mathematics)
In mathematics, a category is an algebraic structure that comprises "objects" that are linked by "arrows". A category has two basic properties: the ability to compose the arrows associatively and the existence of an identity arrow for each object. A simple example is the category of sets, whose objects are sets and whose arrows are functions. On the other hand, any monoid can be understood as a special sort of category, and so can any preorder. In general, the objects and arrows may be abstract entities of any kind, and the notion of category provides a fundamental and abstract way to describe mathematical entities and their relationships. This is the central idea of category theory, a branch of mathematics which seeks to generalize all of mathematics in terms of objects and arrows, independent of what the objects and arrows represent. Virtually every branch of modern mathematics can be described in terms of categories, and doing so often reveals deep insights and similarities between seemingly different areas of mathematics. For more extensive motivational background and historical notes, see category theory and the list of category theory topics.
This page contains text from Wikipedia, the Free Encyclopedia - https://wn.com/Category_(mathematics)
26:20
A Sensible Introduction to Category Theory
Remember when I used a video with a coconut in the thumbnail to drive a stake through the ...
published: 22 Jun 2022
A Sensible Introduction to Category Theory
A Sensible Introduction to Category Theory
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- published: 22 Jun 2022
- views: 449007
Remember when I used a video with a coconut in the thumbnail to drive a stake through the heart of mathematical structure? Today, in this introduction to the basics of category theory, I attempt to remove it.
27 Unhelpful Facts About Category Theory: https://www.youtube.com/watch?v=H0Ek86IH-3Y
MetaMaths on category theory: https://www.youtube.com/watch?v=ZG6t0-JMrw0
My dissertation on the equivalence between the category of monoidal categories and the category of representable multicategories: https://drive.google.com/file/d/1hAkV1qSnUutzQMMQi48yo_fXsgb1YnbL/view?usp=sharing
FURTHER READING
Basic Category Theory (Tom Leinster): https://arxiv.org/pdf/1612.09375.pdf
Categories for the Working Mathematician (Saunders Mac Lane): http://www.mtm.ufsc.br/~ebatista/2016-2/maclanecat.pdf
Category Theory for Computing Science (Michael Barr and Charles Wells): https://www.math.mcgill.ca/triples/Barr-Wells-ctcs.pdf
Category Theory for the Sciences (David Spivak): https://math.mit.edu/~dspivak/CT4S.pdf
Bartosz Milewski on category theory: https://www.youtube.com/watch?v=I8LbkfSSR58&list=PLbgaMIhjbmEnaH_LTkxLI7FMa2HsnawM_
Emily Riehl on category theory: https://www.youtube.com/watch?v=WLkMBMUk48E
MUSIC
Meditation Aquatic
369 (Epidemic Sound)
Nights Full of Overthinking
Lionel Quick (Epidemic Sound)
Oregano
Vendla (Epidemic Sound)
Wash
Timothy Infinite (Epidemic Sound)
Wind
Osoku (Epidemic Sound)
3:16
'Category Is...' Performance w/ Peppermint, Sasha, Trinity & Shea 👯♀️ | RuPaul's Drag Race Season 9
Start the music and gag over Peppermint, Sasha Velour, Trinity Taylor, and Shea Coulee dur...
published: 09 Aug 2018
'Category Is...' Performance w/ Peppermint, Sasha, Trinity & Shea 👯♀️ | RuPaul's Drag Race Season 9
'Category Is...' Performance w/ Peppermint, Sasha, Trinity & Shea 👯♀️ | RuPaul's Drag Race Season 9
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- published: 09 Aug 2018
- views: 14254884
Start the music and gag over Peppermint, Sasha Velour, Trinity Taylor, and Shea Coulee during the 'Category Is' Challenge on RuPaul’s Drag Race Season 9.
#VH1 #DragRace
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0:53
Category Meaning
Video shows what category means. A group, often named or numbered, to which items are assi...
published: 15 Apr 2015
Category Meaning
Category Meaning
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- published: 15 Apr 2015
- views: 76770
Video shows what category means. A group, often named or numbered, to which items are assigned based on similarity or defined criteria.. A collection of objects, together with a transitively closed collection of composable arrows between them, such that every object has an identity arrow, and such that arrow composition is associative.. category synonyms: Wikisaurus:class, class, family, genus, group, kingdom, order, phylum, race, tribe, type. category pronunciation. How to pronounce, definition by Wiktionary dictionary. category meaning. Powered by MaryTTS
25:50
Universal Construction | Category Theory and Why We Care 1.2
To fully utilise the exciting category theory we've learnt so far, we need a way to abstra...
published: 03 Dec 2024
Universal Construction | Category Theory and Why We Care 1.2
Universal Construction | Category Theory and Why We Care 1.2
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- published: 03 Dec 2024
- views: 23955
To fully utilise the exciting category theory we've learnt so far, we need a way to abstract definitions from a specific category and then be able to apply them in any category we want. The solution to this is universal construction.
This video will explore the process of universal construction and see it used in practice, which will further expose some elegant relationships between categories that we've seen before. Taking examples from mathematical proofs, functional programming and beyond, this is the next major step into abstraction that our category theory journey takes us.
― Timestamps ―
0:00 - Intro
1:03 - Isomorphism
5:22 - Terminal object
10:41 - Universal construction
12:27 - Conjunction
17:32 - Product
18:29 - Pair type
24:12 - Outro
25:00 - Exercise
― Credits ―
All animation and voiceover created by Eyesomorphic.
Background music: 'Sonder', composed by Caleb Peppiatt.
― Further Reading ―
Category Theory and Why We Care, by Eyesomorphic (Lecture series): https://youtube.com/playlist?list=PLoCKNPo3VR0I2wqT2wemCNIlpjdy_Ry_q&si=9UOLXRFqNdfgGXlI
Algebra: Chapter 0 (Book), by Paulo Aluffi
4:13
ONE N’ ONLY／“Category” Music Video
【ファンクラブツアー】
ONE N’ ONLY FC TOUR 2024 ～SWAG祭～
2024.8.22(木)大阪：Zepp Namba (OSAKA)
2024.8.23(金...
published: 23 Aug 2019
ONE N’ ONLY／“Category” Music Video
ONE N’ ONLY／“Category” Music Video
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- published: 23 Aug 2019
- views: 3916980
【ファンクラブツアー】
ONE N’ ONLY FC TOUR 2024 ～SWAG祭～
2024.8.22(木)大阪：Zepp Namba (OSAKA)
2024.8.23(金)愛知：Zepp Nagoya
2024.8.26(月)-27(火)東京：Zepp Haneda (TOKYO)
https://one-n-only.jp/live/live30214/
【グループ史上最大規模のツアー】
ONE N’ SWAG 2024 ¿Fiesta?
2024.9.27(金)-28(土)東京：東京国際フォーラム ホールC
2024.10.14(月祝)愛知：Niterra日本特殊陶業市民会館 フォレストホール
2024.11.15(金)大阪：大阪国際会議場(グランキューブ大阪)
2024年11月15日(金) 開場17:30／開演18:30
2025.1.18(土)東京：東京ガーデンシアター
https://one-n-only.jp/live/live30130/
【New Release!!】
3rd EP「Fiesta」
https://one-n-only.jp/news/news30371/
2024.4.10（wed）
ONE N’ ONLY ／ DOMINO
https://ssm.lnk.to/DOMINO_ONO
2024.3.1（fri）
ONE N’ ONLY ／ TALKIN'
https://ssm.lnk.to/TALKIN
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スターダストプロモーション所属の6人組の男性グループ。
ボーカルTETTA（1997年11月24日生まれ）、REI（1997年1月2日生まれ）、EIKU（1999年12月19日生まれ）。ラップ&ダンサーHAYATO（1999年9月17日生まれ）、KENSHIN（1999年7月8日生まれ）、NAOYA（1998年4月6日生まれ）からなる6人組。デビュー以来"JK-POP"という独自のスタイルで活動していき、2023年の南米ワンマンツアーを経て、Latin カルチャーを取り込み"JK-Pop"と"Latin Music"を融合した、さらなる独自のスタイル"Jatin Pop"へと進化し、唯一無二のスタイルを貫き続けるダンス&ボーカルグループ。
Music Videoは世界各国注目され、南米・アジア圏・欧州からのアクセスが殺到し、合計再生回数は3000万回を突破！TikTokフォロワー数は、日本人男性音楽アーティストでは1位となる580万人超え! 動画の総再生回数は6.2億回を突破!!
2022年7月にはブラジルで開催された南米最大のアニメフェス『Anime Friends 2022』で初の海外パフォーマンスを成功させ、2023年4月にはワンマンでのラテンアメリカツアー「LATIN TOUR 2023」を開催した。
2023年10月より47都道府県ツアー『ONE N’ SWAG ～Hook Up!!!!!!～』を開催。ツアーファイナルとなるパシフィコ横浜公演を含む全47公演がソールドアウトした。
ONE N’ ONLY is a six-piece boy band comprised of TETTA, REI, EIKU, HAYATO, KENSHIN, and NAOYA. Formed by renown Japanese talent agency Stardust Promotion, the members were originally from two separate bands, EBiSSH and SBC (Satori Boys Club).
Since their debut in 2018, they’ve boasted their unique ability to blend genres, starting with JK-POP. They have since evolved to Jatin Pop, a blend of Japanese and Latin pop, after finding international TikTok success.
The band’s music videos have garnered views from Asia, Latin and North America, and Europe, with a total view count exceeding 30 million. They are Japan’s Number 1 most followed male musical artist on TikTok with over 5.8 million followers and 620 million views.
In 2022, the band performed overseas for the first time at South America’s largest Anime event, Anime Friends 2022. In the following year, they embarked on their headlining LATIN TOUR 2023. Later in 2023, the band toured across all 47 of Japan’s prefectures, closing their tour with a sold-out show at Pacifico Yokohama.
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#ワンエン #ONENONLY #ONO #ワンエンTV
0:16
Category is: PRECISION 💂✨
Follow us on:
TikTok: https://www.tiktok.com/@rockettes
Instagram: https://www.instagram.c...
published: 27 Oct 2024
Category is: PRECISION 💂✨
Category is: PRECISION 💂✨
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- published: 27 Oct 2024
- views: 2455808
Follow us on:
TikTok: https://www.tiktok.com/@rockettes
Instagram: https://www.instagram.com/therockettes
Facebook: https://www.facebook.com/rockettes/
Twitter: https://twitter.com/Rockettes
Threads: https://www.threads.net/@therockettes
Visit our website for the latest from the kickline: https://www.rockettes.com/
#Rockettes #Shorts #Kickline
46:46
Category Theory 1.1: Motivation and Philosophy
Motivation and philosophy
published: 25 Aug 2016
Category Theory 1.1: Motivation and Philosophy
Category Theory 1.1: Motivation and Philosophy
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- published: 25 Aug 2016
- views: 348092
Motivation and philosophy
3:26
Lil Durk & Tee Grizzley "Category Hoes" (Official Audio)
Listen to the official audio of "Category Hoes" by Lil Durk & Tee Grizzley.
Subscribe to ...
published: 08 Dec 2017
Lil Durk & Tee Grizzley "Category Hoes" (Official Audio)
Lil Durk & Tee Grizzley "Category Hoes" (Official Audio)
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- published: 08 Dec 2017
- views: 905153
Listen to the official audio of "Category Hoes" by Lil Durk & Tee Grizzley.
Subscribe to Lil Durk's official channel for exclusive music videos and behind the scenes looks: http://bit.ly/Subscribe-to-Durk
More Lil Durk:
https://fb.com/lildurk
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0:48
Won in wedding cake category ✨✨
Won in wedding cake category ✨✨
Overjoyed to announce that I won in the Wedding Cake Cate...
published: 17 Dec 2024
Won in wedding cake category ✨✨
Won in wedding cake category ✨✨
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- published: 17 Dec 2024
- views: 245
Won in wedding cake category ✨✨
Overjoyed to announce that I won in the Wedding Cake Category at the India Bake Show 2024, held in Bengaluru! It’s been an incredible journey perfecting every detail, and this recognition means the world to me. Thank you to everyone who has believed in me and my work—your support makes every win even more special!”
#cakesandbakeschool #shortsvideo #ytshorts #weddingcake
0:19
Category is.....animals! 🐈 🐇 🐄
#animal #categories #head2head #breadbasket
published: 14 Sep 2024
Category is.....animals! 🐈 🐇 🐄
Category is.....animals! 🐈 🐇 🐄
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- published: 14 Sep 2024
- views: 152046
#animal #categories #head2head #breadbasket
A Sensible Introduction to Category Theory...
'Category Is...' Performance w/ Peppermint, Sasha,...
Category Meaning...
Universal Construction | Category Theory and Why W...
ONE N’ ONLY／“Category” Music Video...
Category is: PRECISION 💂✨...
Category Theory 1.1: Motivation and Philosophy...
Lil Durk & Tee Grizzley "Category Hoes" (Official ...
Won in wedding cake category ✨✨...