Type: Article

Graded and Koszul categories

Roberto Martínez-Villa; Oyvind Solberg;

Abstract:

Koszul algebras have arisen m many contexts, algebraic geometry, combinatorics, Lie algebras, non-commutative geometry and topology The aim of this paper and several sequel papers is to show that for any finite dimensional algebra there is always a naturally associated Koszul theory To obtain this, the notions of Koszul algebras, linear modules and Koszul duality are extended to additive (graded) categories over a field The main focus of this paper is to provide these generalizations and the necessary preliminaries