Combinatorial categories and permutation groups - Jones, Gareth A. (Ars mathematica contemporanea, 2016)
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 ?$Γ$? , with automorphism group isomorphic to ?$Γ / N$?. 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 ?$\mathcal{U}(G)$?, and how the outer automorphism group of ?$Γ$? acts on them. Examples constructed include kaleidoscopic maps with trinity symmetry.
Keywords: category; covering space; kategorija; krovni prostor; permutacijska grupa; permutation group; regular hypermap; regular map; regularni hiperzemljevid; regularni zemljevid