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Graded and Koszul Categories

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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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Authors and Affiliations

  1. Instituto de Matemáticas, Universidad Nacional Autonoma de Mexico, Campus Morelia, Apartado Postal 27-3 (Xangari), C.P. 58089, Morelia, Michoacán, Mexico

    Roberto Martínez-Villa

  2. Institutt for Matematiske Fag, NTNU, 7034, Trondheim, Norway

    Øyvind Solberg

Authors
  1. Roberto Martínez-Villa
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  2. Øyvind Solberg
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Correspondence to Øyvind Solberg.

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Martínez-Villa, R., Solberg, Ø. Graded and Koszul Categories. Appl Categor Struct 18, 615–652 (2010). https://doi.org/10.1007/s10485-009-9191-6

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  • DOI: https://doi.org/10.1007/s10485-009-9191-6

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