An automorphism of an object in a category is an isomorphism . In other words, an automorphism is an endomorphism that is an isomorphism.
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.
(…)
Permutations are automorphisms in FinSet.
automorphism group
Discussion of automorphism groups internal to sheaf toposes (“automorphism sheaves”):
Robert Friedman, John W. Morgan, §2.1 in: Automorphism sheaves, spectral covers, and the Kostant and Steinberg sections [arXiv:math/0209053]
Last revised on September 23, 2023 at 23:42:58. See the history of this page for a list of all contributions to it.