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Article Dans Une Revue Documenta Mathematica Année : 2006

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

Résumé

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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Dates et versions

hal-00004260 , version 1 (15-02-2005)

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Claude Cibils, Andrea Solotar. Galois coverings, Morita equivalence and smash extensions of categories over a field. Documenta Mathematica, 2006, 11, pp.143--159. ⟨hal-00004260⟩
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