We give a description of the indecomposable objects in the derived category of a finite-dimensional skewed-gentle algebra.

In this paper we study d-Koszul algebras which were introduced by Berger. We show that when d ¿ 3, these are classiÿed by the Ext-algebra being generated in degrees 0, 1, and 2. We show the Ext-algebra, after regrading, is a Koszul algebra and present the structure of the Ext-algebra.

Abstract. 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 and we show that these constructions agree with the usual ones for algebras. In the case of the smash product for an infinite group our construction specialized for a ring agrees with M. Beattie's construction of a ring with local units. We recover in a categorical generalized setting the Duality Theorems of M. Cohen and S. Montgomery (1984), and we provide a unification with the results on coverings of quivers and relations by E. Green (1983). We obtain a confirmation in a quiver and relations-free categorical setting that both constructions 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 representation theories of a category and of a Galois cover of it.

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In this paper we continue the study of stratifying systems, which were introduced by K. Erdmann and C. Sáenz in [Comm. Algebra 31 (7) (2003) 3429-3446]. We show that this new concept provides a categorical generalization of the ∆-modules for a standardly stratified algebra.