• DOI:10.1090/proc/15949
• Corpus ID: 219720879

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}
}

• Maximilien P'eroux
• Published 16 June 2020
• Mathematics
• arXiv: Algebraic Topology

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 coalgebras associated to a monoidal model category and we show that these coalgebras cannot be rigidified. That is, their $\infty$-categories are not equivalent to the Dwyer-Kan localizations of strict coalgebras in the usual monoidal model categories of spectra and of connective discrete $R$-modules.