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Koszul duality for compactly generated derived categories of second kind

Research output: Contribution to Journal/MagazineJournal articlepeer-review

Published
<mark>Journal publication date</mark>7/12/2021
<mark>Journal</mark>Journal of Noncommutative Geometry
Issue number4
Volume15
Number of pages17
Pages (from-to)1355-1371
Publication StatusPublished
<mark>Original language</mark>English

Abstract

For any dg algebra A we construct a closed model category structure on dg A-modules such that the corresponding homotopy category is compactly generated by dg A-modules that are finitely generated and free over A (disregarding the differential). We prove that this closed model category is Quillen equivalent to the category of comodules over a certain, possibly nonconilpotent dg coalgebra, a so-called extended bar construction of A. This generalises and complements certain aspects of dg Koszul duality for associative algebras.