Given a set and a subset of , the inclusion function of in is the function given by
for every element of that belongs to .
Every inclusion function is an injection, and every injection is isomorphic (in the slice category ) to an inclusion function. In appropriate categories, it is common to analogously interpret monomorphisms or regular monomorphisms as inclusions of subobjects. One then speaks of inclusion morphisms.
The inclusion function of in is the restriction to of the identity function on . Conversely, the restriction to of any function is the composite of after the inclusion function:
Revised on August 9, 2010 21:46:21
by Toby Bartels