Combinatorial categories and permutation groups
Combinatorics
2013-09-25 v1 Group Theory
Abstract
The regular objects in various categories, such as maps, hypermaps or covering spaces, can be identified with the normal subgroups N of a given group \Gamma, with quotient group isomorphic to \Gamma/N. It is shown how to enumerate such objects with a given finite automorphism group G, how to represent them all as quotients of a single regular object U(G), and how they are acted on by the outer automorphism group of \Gamma. Examples constructed include kaleidoscopic maps with trinity symmetry.
Cite
@article{arxiv.1309.6119,
title = {Combinatorial categories and permutation groups},
author = {Gareth A. Jones},
journal= {arXiv preprint arXiv:1309.6119},
year = {2013}
}