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Inclusion map
Set-theoretic function / From Wikipedia, the free encyclopedia
In mathematics, if is a subset of
then the inclusion map is the function
that sends each element
of
to
treated as an element of
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An inclusion map may also referred to as an inclusion function, an insertion,[1] or a canonical injection.
A "hooked arrow" (U+21AA ↪ RIGHTWARDS ARROW WITH HOOK)[2] is sometimes used in place of the function arrow above to denote an inclusion map; thus:
(However, some authors use this hooked arrow for any embedding.)
This and other analogous injective functions[3] from substructures are sometimes called natural injections.
Given any morphism between objects
and
, if there is an inclusion map
into the domain
, then one can form the restriction
of
In many instances, one can also construct a canonical inclusion into the codomain
known as the range of