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arXiv · 1909.11399

Koszul duality for compactly generated derived categories of second kind

Ai Guan·Andrey Lazarev
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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.

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Ai Guan, Andrey Lazarev. 2022-05-11. Koszul duality for compactly generated derived categories of second kind. https://doi.org/10.4171/jncg%2F438

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