Galois coverings, Morita equivalence and smash extensions of categories over a field.
Claude CibilsDépartement de Mathématiques Departemento de Matemática Université de Montpellier 2 Facultad de Ciencias F-34095 Montpellier cedex 5 Exactas y Naturales France Universidad de Buenos Aires
Andrea SolotarCiudad Universitaria, Pabellón 1 1428, Buenos Aires, Argentina
Algebras over a field generalize to categories over in order to considers Galois coverings. Two theories presenting analogies, namely smash extensions and Galois coverings with respect to a finite group are known to be different. However we prove in this paper that they are Morita equivalent. For this purpose we need to describe explicit processes providing Morita equivalences of categories which we call contraction and expansion. A structure theorem is obtained: composition of these processes provides any Morita equivalence up to equivalence, a result which is related with the karoubianisation (or idempotent completion) and additivisation of a -category.
Cite this article
Claude Cibils, Andrea Solotar, Galois coverings, Morita equivalence and smash extensions of categories over a field.. Doc. Math. 11 (2006), pp. 143–159DOI 10.4171/DM/207