Graded and Koszul categories

Details Graded and Koszul categories Graded and Koszul categories

2009-02-04

arxiv.org/abs/0902.0714v1

Mathematics

Category Theory

34 pages

Scientific paper

Koszul algebras have arisen in 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.

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