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 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 U ( G ) , and how the outer automorphism group of Γ acts on them. Examples constructed include kaleidoscopic maps with trinity symmetry.
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