Graded and Koszul categories
Roberto Martinez-Villa, {\O}yvind Solberg

TL;DR
This paper extends the concepts of Koszul algebras, modules, and duality from finite-dimensional algebras to additive graded categories, providing foundational generalizations for broader mathematical contexts.
Contribution
It introduces a framework for associating Koszul theory with any finite-dimensional algebra via additive graded categories, expanding the scope of Koszul duality.
Findings
Generalization of Koszul algebras to additive categories
Extension of linear modules and duality concepts
Preliminaries for future applications in various mathematical fields
Abstract
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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Taxonomy
TopicsAlgebraic structures and combinatorial models · Advanced Topics in Algebra · Homotopy and Cohomology in Algebraic Topology
