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  • CategoricalKoszulDualityV5

    Rights statement: 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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Categorical Koszul Duality

Research output: Contribution to Journal/Magazine › Journal article › peer-review

Published
Article number108644
<mark>Journal publication date</mark>30/11/2022
<mark>Journal</mark>Advances in Mathematics
Issue numberPart B
Volume409
Number of pages52
Publication StatusPublished
Early online date31/08/22
<mark>Original language</mark>English

Abstract

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.

Bibliographic note

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