Gradings, smash products and Galois coverings of a small category

Details Gradings, smash products and Galois coverings of a small category Gradings, smash products and Galois coverings of a small category

2012-03-27

arxiv.org/abs/1203.5905v1

Mathematics

Category Theory

19 pages

Scientific paper

In this paper we develop the theory of coverings of a small connected category B. We show that the category of Galois coverings of B is equivalent to the category of Galois coverings of its fundamental groupoid. Making use of effective gradings of B we explicitly construct Galois coverings through a smash product analogous to the one considered in the linear case. In particular, the universal cover of B can be obtained from its fundamental groupoid.

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