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Sergey Arkhipov

Homotopy limits in the category of dg-categories in terms of A-comodules

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Homotopy limits in the category of dg-categories in terms of A-comodules. / Arkhipov, Sergey; Ørsted, Sebastian.

In: European Journal of Mathematics, Vol. 7, No. 2, 06.2021, p. 671-705.

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Arkhipov, Sergey ; Ørsted, Sebastian. / Homotopy limits in the category of dg-categories in terms of A-comodules. In: European Journal of Mathematics. 2021 ; Vol. 7, No. 2. pp. 671-705.

Bibtex

@article{83ef79abcc5a4edca70864da65a8bb45,
title = "Homotopy limits in the category of dg-categories in terms of A∞-comodules",
abstract = "We apply an explicit construction of a simplicial powering in dg-categories, due to Holstein (Properness and simplicial resolutions for the model category dgCat, 2014. arXiv:1403.4381) and Arkhipov and Poliakova (Homol Homotopy Appl 22(2):151–162, 2019), as well as our own results on homotopy ends (Arkhipov and {\O}rsted in Homotopy (co)limits via homotopy (co)ends in general combinatorial model categories, 2018. arXiv:1807.03266), to obtain an explicit model for the homotopy limit of a cosimplicial system of dg-categories. We apply this to obtain a model for homotopy descent in terms of A ∞-comodules, proving a conjecture by Block et al. (Homol Homotopy Appl 19(2):343–371, 2017) in the process.",
keywords = "Algebraic geometry, Category theory, Derived categories, Homotopical algebraic geometry",
author = "Sergey Arkhipov and Sebastian {\O}rsted",
note = "Publisher Copyright: {\textcopyright} 2021, Springer Nature Switzerland AG. Copyright: Copyright 2021 Elsevier B.V., All rights reserved.",
year = "2021",
month = jun,
doi = "10.1007/s40879-020-00439-4",
language = "English",
volume = "7",
pages = "671--705",
journal = "European Journal of Mathematics",
issn = "2199-675X",
publisher = "Springer",
number = "2",

}

RIS

TY - JOUR

T1 - Homotopy limits in the category of dg-categories in terms of A∞-comodules

AU - Arkhipov, Sergey

AU - Ørsted, Sebastian

N1 - Publisher Copyright: © 2021, Springer Nature Switzerland AG. Copyright: Copyright 2021 Elsevier B.V., All rights reserved.

PY - 2021/6

Y1 - 2021/6

N2 - We apply an explicit construction of a simplicial powering in dg-categories, due to Holstein (Properness and simplicial resolutions for the model category dgCat, 2014. arXiv:1403.4381) and Arkhipov and Poliakova (Homol Homotopy Appl 22(2):151–162, 2019), as well as our own results on homotopy ends (Arkhipov and Ørsted in Homotopy (co)limits via homotopy (co)ends in general combinatorial model categories, 2018. arXiv:1807.03266), to obtain an explicit model for the homotopy limit of a cosimplicial system of dg-categories. We apply this to obtain a model for homotopy descent in terms of A ∞-comodules, proving a conjecture by Block et al. (Homol Homotopy Appl 19(2):343–371, 2017) in the process.

AB - We apply an explicit construction of a simplicial powering in dg-categories, due to Holstein (Properness and simplicial resolutions for the model category dgCat, 2014. arXiv:1403.4381) and Arkhipov and Poliakova (Homol Homotopy Appl 22(2):151–162, 2019), as well as our own results on homotopy ends (Arkhipov and Ørsted in Homotopy (co)limits via homotopy (co)ends in general combinatorial model categories, 2018. arXiv:1807.03266), to obtain an explicit model for the homotopy limit of a cosimplicial system of dg-categories. We apply this to obtain a model for homotopy descent in terms of A ∞-comodules, proving a conjecture by Block et al. (Homol Homotopy Appl 19(2):343–371, 2017) in the process.

KW - Algebraic geometry

KW - Category theory

KW - Derived categories

KW - Homotopical algebraic geometry

UR - http://www.scopus.com/inward/record.url?scp=85102427475&partnerID=8YFLogxK

U2 - 10.1007/s40879-020-00439-4

DO - 10.1007/s40879-020-00439-4

M3 - Journal article

AN - SCOPUS:85102427475

VL - 7

SP - 671

EP - 705

JO - European Journal of Mathematics

JF - European Journal of Mathematics

SN - 2199-675X

IS - 2

ER -