An automorphism of an object in a category is an isomorphism . In other words, an automorphism is an isomorphism that is an endomorphism.
Given an object , the automorphisms of form a group under composition, the automorphism group of , which is a submonoid of the endomorphism monoid of :
which may be written if the category is understood. Up to equivalence, every group is an automorphism group; see delooping.
Revised on November 1, 2013 06:43:02
by Urs Schreiber