Homotopy limits in the category of dg-categories in terms of ${\mathrm{A}}_{\infty }$-comodules

Abstract

In this paper, we apply an explicit construction of a simplicial powering in dg-categories, due to Holstein (2016) and Arkhipov and Poliakova (2018), as well as our own results on homotopy ends (Arkhipov and Ørsted 2018), 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 ${\mathrm{A}}_{\infty }$-comodules, proving a conjecture by Block, Holstein, and Wei (2017) in the process.

31 pages; updated a reference