Koszul duality for compactly generated derived categories of second kind

Guan, Ai and Lazarev, Andrey (2021) Koszul duality for compactly generated derived categories of second kind. Journal of Noncommutative Geometry, 15 (4). pp. 1355-1371. ISSN 1661-6952

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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.