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, Contemporary Mathematics 322 (2003) 217-244 [arXiv:math/0209053]
Simon Henry (2017) [MO:a/262687]
Last revised on June 26, 2024 at 07:13:38. See the history of this page for a list of all contributions to it.