In mathematics, if is a subset of , then the inclusion map (also inclusion function, insertion, or canonical injection) is the function that sends each element, of to , treated as an element of :
A "hooked arrow" is sometimes used in place of the function arrow above to denote an inclusion map.
This and other analogous injective functions from substructures are sometimes called natural injections.
Given any morphismf between objectsX and Y, if there is an inclusion map into the domain, then one can form the restrictionfi of f. In many instances, one can also construct a canonical inclusion into the codomainR→Y known as the range of f.
Applications of inclusion maps
Inclusion maps tend to be homomorphisms of algebraic structures; thus, such inclusion maps are embeddings. More precisely, given a sub-structure closed under some operations, the inclusion map will be an embedding for tautological reasons. For example, for a binary operation , to require that
is simply to say that is consistently computed in the sub-structure and the large structure. The case of a unary operation is similar; but one should also look at nullary operations, which pick out a constant element. Here the point is that closure means such constants must already be given in the substructure.
The inclusion of these points promises more diversity of environments, ranging from urban city streets to isolated, swampy areas.Below is a comparison of the leaked GTA 6 map and the GTA 5 map, shared ...
The telescope's infrared detectors will be able to distinguish 102 colors invisible to the human eye, yielding the most colorful, inclusive map ever made of the cosmos.
... disability, and social inclusion (GEDSI). The document will serve as a reference for local governments to determine a strategy map and policy for a just and inclusive transition to low-carbon energy.
Jakarta (ANTARA) - The Ministry of Primary and Secondary Education has highlighted that stigma is still posing a challenge to realizing inclusive early childhood education ... Nusantara education road map supports inclusive schools.
The telescope’s infrared detectors will be able to distinguish 102 colors invisible to the human eye, yielding the most colorful, inclusive map ever made of the cosmos.
The telescope’s infrared detectors will be able to distinguish 102 colors invisible to the human eye, yielding the most colorful, inclusive map ever made of the cosmos.
The telescope’s infrared detectors will be able to distinguish 102 colors invisible to the human eye, yielding the most colorful, inclusive map ever made of the cosmos.
The telescope’s infrared detectors will be able to distinguish 102 colors invisible to the human eye, yielding the most colorful, inclusive map ever made of the cosmos.
While entire divisions at GM focus on deploying its advanced driver-assist technology, only one man is known as the chief of maps ... “My job is finding specifications for how to build the map and determining exactly what needs to happen ... Geo-inclusive.
File photo. Soller is set to introduce innovative new measures to manage overtourism ... The secondary streets inclusive of the old town will also be affected, according to a new map of the exclusion zone ... Panoramic view of Port de Soller, Mallorca ... .
... map ... While there’s been no official news about its inclusion in season 3, insider CharlieIntel recently reported that a number of content creators had been playtesting the fan-favourite map.
"In years since then, historical maps from various European cartographers from the 1500s to the 1800s recognized the inclusion of Palawan Island in the Philippine archipelago as administered by the ...
During the session, the parties discussed that RS Berkane's shirts displayed a map of Morocco, including the territory of Western Sahara, an inclusion that does not align with the official ...
The SAF-backed authorities have presented their own road map for ending the war that includes an inclusive national dialogue, the formation of a caretaker transitional government and the selection of a civilian prime minister.
This system leverages advanced mapping technology by integrating both 2D and 3D capabilities. The inclusion of 2D mapping provides a rapid, overhead view of the environment to gain quick ...
is a 
, then the inclusion map (also inclusion function, insertion, or canonical injection) is the 
that sends each element, 
of 
is sometimes used in place of the function arrow above to denote an inclusion map.
, then one can form the 
, to require that
Chatanooga Times Free Press
13 Mar 2025
Chatanooga Times Free Press
13 Mar 2025