Galois coverings, Morita equivalence and smash extensions of categories over a field

Details Galois coverings, Morita equivalence and smash extensions of categories over a field Galois coverings, Morita equivalence and smash extensions of categories over a field

2005-02-15

arxiv.org/abs/math/0502308v1

Mathematics

Rings and Algebras

Scientific paper

We consider categories over a field $k$ in order to prove that smash extensions and Galois coverings with respect to a finite group coincide up to Morita equivalence of $k$-categories. For this purpose we describe processes providing Morita equivalences called contraction and expansion. We prove that composition of these processes provides any Morita equivalence, a result which is related with the karoubianisation (or idempotent completion) and additivisation of a $k$-category.

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