Geodesic
Combinatorial categories and permutation groups
Ars Mathematica Contemporanea, Tome 10 (2016) no. 2, pp. 237-254.

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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.
DOI : 10.26493/1855-3974.545.fd5
Keywords: Regular map, regular hypermap, covering space, permutation group, category 
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Gareth A. Jones. Combinatorial categories and permutation groups. Ars Mathematica Contemporanea, Tome 10 (2016) no. 2, pp. 237-254. doi : 10.26493/1855-3974.545.fd5. http://geodesic.mathdoc.fr/articles/10.26493/1855-3974.545.fd5/

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