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Koszul duality for compactly generated derived categories of second kind

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Koszul duality for compactly generated derived categories of second kind. / Guan, Ai; Lazarev, Andrey.
In: Journal of Noncommutative Geometry, Vol. 15, No. 4, 07.12.2021, p. 1355-1371.

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

Harvard

Guan, A & Lazarev, A 2021, 'Koszul duality for compactly generated derived categories of second kind', Journal of Noncommutative Geometry, vol. 15, no. 4, pp. 1355-1371. https://doi.org/10.4171/jncg/438

APA

Guan, A., & Lazarev, A. (2021). Koszul duality for compactly generated derived categories of second kind. Journal of Noncommutative Geometry, 15(4), 1355-1371. https://doi.org/10.4171/jncg/438

Vancouver

Guan A, Lazarev A. Koszul duality for compactly generated derived categories of second kind. Journal of Noncommutative Geometry. 2021 Dec 7;15(4):1355-1371. doi: 10.4171/jncg/438

Author

Guan, Ai ; Lazarev, Andrey. / Koszul duality for compactly generated derived categories of second kind. In: Journal of Noncommutative Geometry. 2021 ; Vol. 15, No. 4. pp. 1355-1371.

Bibtex

@article{e3c2215afae04b46882c5842f8752feb,
title = "Koszul duality for compactly generated derived categories of second kind",
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.",
author = "Ai Guan and Andrey Lazarev",
year = "2021",
month = dec,
day = "7",
doi = "10.4171/jncg/438",
language = "English",
volume = "15",
pages = "1355--1371",
journal = "Journal of Noncommutative Geometry",
issn = "1661-6952",
publisher = "European Mathematical Society Publishing House",
number = "4",

}

RIS

TY - JOUR

T1 - Koszul duality for compactly generated derived categories of second kind

AU - Guan, Ai

AU - Lazarev, Andrey

PY - 2021/12/7

Y1 - 2021/12/7

N2 - 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.

AB - 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.

U2 - 10.4171/jncg/438

DO - 10.4171/jncg/438

M3 - Journal article

VL - 15

SP - 1355

EP - 1371

JO - Journal of Noncommutative Geometry

JF - Journal of Noncommutative Geometry

SN - 1661-6952

IS - 4

ER -