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

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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.

Original languageEnglish
JournalEuropean Journal of Mathematics
Volume7
Issue2
Pages (from-to)671-705
Number of pages35
ISSN2199-675X
DOIs
Publication statusPublished - Jun 2021

Bibliographical note

Publisher Copyright:
© 2021, Springer Nature Switzerland AG.

Copyright:
Copyright 2021 Elsevier B.V., All rights reserved.

    Research areas

  • Algebraic geometry, Category theory, Derived categories, Homotopical algebraic geometry

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