Geodesic
Galois coverings, Morita equivalence and smash extensions of categories over a field.
Documenta mathematica, Tome 11 (2006), pp. 143-159
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Algebras over a field k generalize to categories over k 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 k-category.
DOI : 10.4171/dm/207
Classification : 16D90, 16S40, 16W50, 18E05
Mots-clés : Morita theory, Galois covering, Hopf algebra, completion, k-category, smash product, karoubianisation 
@article{10_4171_dm_207,
     author = {Claude Cibils and Andrea Solotar},
     title = {Galois coverings, {Morita} equivalence and smash extensions of categories over a field.},
     journal = {Documenta mathematica},
     pages = {143--159},
     year = {2006},
     volume = {11},
     doi = {10.4171/dm/207},
     url = {http://geodesic.mathdoc.fr/articles/10.4171/dm/207/}
}
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Claude Cibils; Andrea Solotar. Galois coverings, Morita equivalence and smash extensions of categories over a field.. Documenta mathematica, Tome 11 (2006), pp. 143-159. doi: 10.4171/dm/207

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