Differential graded Koszul duality: an introductory survey

Leonid Positselski

Differential graded Koszul duality: an introductory survey

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arxiv 2207.07063 v5 pith:EOTBPRP5 submitted 2022-07-14 math.CT math.HOmath.RA

Leonid Positselski This is my paper · ORCID

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keywords dualitykoszularxivauthorcdg-comodulescdg-contramodulescovariantcurved

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This is an overview on derived nonhomogeneous Koszul duality over a field, mostly based on the author's memoir arXiv:0905.2621. The paper is intended to serve as a pedagogical introduction and a summary of the covariant duality between DG-algebras and curved DG-coalgebras, as well as the triality between DG-modules, CDG-comodules, and CDG-contramodules. Some personal reminiscences are included as a part of historical discussion.

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Coderived and contraderived categories for a cotorsion pair, flat-type cotorsion pairs, and relative periodicity
math.CT 2025-09 conditional novelty 7.0 of 10

For hereditary complete cotorsion pairs generated by a set in a Grothendieck category, the coderived category of the left class is equivalent to the contraderived category of the right class, and for sandwiched pairs ...

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