Graded and Koszul categories (Q613569)

Koszul algebras have arisen in many contexts: algebraic geometry, combinatorics, Lie algebras, non-commutative geometry and topology. The authors intend to generalize the classical Koszul theory to any finite-dimensional algebras. For this purpose, they establish Koszul theories for additive (graded) categories over a field. Some necessary notations and basic properties for this theory are presented in this paper.