Combinatorial categories and permutation groups
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 , with quotient group isomorphic to /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 . Examples constructed include kaleidoscopic maps with trinity symmetry.
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