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Pré-Publication, Document De Travail Année : 2003

Skew category, Galois covering and smash product of a category over a ring

Eduardo N. Marcos
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Résumé

In this paper we consider categories over a commutative ring provided either with a free action or with a grading of a not necessarily finite group. We define the smash product category and the skew category of a graded category. We show that those constructions agree with the usual ones for algebras. In case of the smash product for an infinitegroup our construction specialized for a ring agrees with M. Beattie's construction of a ring with local units in. We recover in a categorical generalized setting the duality theorems of M. Cohen and S. Montgomery and we provide a unification with the results on coverings of quivers and relations by E. Green. We obtain a confirmation in a quiver and relations free categorical setting that twoconstructions are mutual inverses, namely the quotient of a free action category and the smash product of a graded category. Finally we describe functorial relations between the representations theories of a category and of a Galois cover of it.
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Dates et versions

hal-00000938 , version 1 (10-12-2003)
hal-00000938 , version 2 (22-12-2003)
hal-00000938 , version 3 (10-09-2004)

Identifiants

Citer

Claude Cibils, Eduardo N. Marcos. Skew category, Galois covering and smash product of a category over a ring. 2003. ⟨hal-00000938v1⟩
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