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Coalgebras in the Dwyer-Kan localization of a model category
We show that weak monoidal Quillen equivalences induce equivalences of symmetric monoidal $\infty$-categories with respect to the Dwyer-Kan localization of the symmetric monoidal model categories. The result will induce a Dold-Kan correspondance of coalgebras in $\infty$-categories. Moreover it shows that Shipley's zig-zag of Quillen equivalences provides an explicit symmetric monoidal …