# Coalgebras in the Dwyer-Kan localization of a model category

@article{Peroux2020CoalgebrasIT, title={Coalgebras in the Dwyer-Kan localization of a model category}, author={Maximilien P'eroux}, journal={arXiv: Algebraic Topology}, year={2020} }

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 equivalence of $\infty$-categories for the stable Dold-Kan correspondance. We study homotopy coherent…

## 3 Citations

Admissible replacements for simplicial monoidal model categories.

- Mathematics
- 2020

Using Dugger's construction of universal model categories, we produce replacements for simplicial and combinatorial symmetric monoidal model categories with better operadic properties. Namely, these…

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