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.
