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In this paper, we apply an explicit construction of a simplicial powering indg-categories, due to Holstein (2016) and Arkhipov and Poliakova (2018), aswell as our own results on homotopy ends (Arkhipov and {\O}rsted 2018), toobtain an explicit model for the homotopy limit of a cosimplicial system ofdg-categories. We apply this to obtain a model for homotopy descent in terms of$\mathrm{A}_{\infty}$-comodules, proving a conjecture by Block, Holstein, andWei (2017) in the process.

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