Galois coverings of enriched categories and an extension of Cohen-Montgomery theorem

Abstract

The purpose of this paper is to give an intrinsic fundamental group and coverings for categories enriched over an abelian symmetric monoidal category (V,⊗,I). We relate this to various categorical constructions such as the universal covering, smash products and connected gradings of a small V-category B. Finally, we apply these methods to obtain an extension of Cohen-Montgomery duality theorem for coactions to the symmetric monoidal category (V,⊗,I).