Categorical Koszul Duality

Holstein, Julian and Lazarev, Andrey (2022) Categorical Koszul Duality. Advances in Mathematics, 409 (Part B). ISSN 0001-8708

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In this paper we establish Koszul duality between dg categories and a class of curved coalgebras, generalizing the corresponding result for dg algebras and conilpotent curved coalgebras. We show that the normalized chain complex functor transforms the Quillen equivalence between quasicategories and simplicial categories into this Koszul duality. This allows us to give a conceptual interpretation of the dg nerve of a dg category and its adjoint. As an application, we prove that the category of representations of a quasicategory K is equivalent to the coderived category of comodules over C (K), the chain coalgebra of K. A corollary of this is a characterization of the category of constructible dg sheaves on a stratified space as the coderived category of a certain dg coalgebra.

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Journal Article
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Advances in Mathematics
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This is the author’s version of a work that was accepted for publication in Advances in Mathematics. Changes resulting from the publishing process, such as peer review, editing, corrections, structural formatting, and other quality control mechanisms may not be reflected in this document. Changes may have been made to this work since it was submitted for publication. A definitive version was subsequently published in Advances in Mathematics, 409, 108644 , 2022 DOI: 10.1016/j.aim.2022.108644
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06 Sep 2022 08:35
Last Modified:
30 Sep 2023 00:45