Coalgebras in the Dwyer-Kan localization of a model category

  title={Coalgebras in the Dwyer-Kan localization of a model category},
  author={Maximilien P'eroux},
  journal={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… 
3 Citations

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On a Quillen adjunction between the categories of differential graded and simplicial coalgebras

  • W. H. B. Sore
  • Mathematics
    Journal of Homotopy and Related Structures
  • 2018
We prove that the normalization functor of the Dold-Kan correspondence does not induce a Quillen equivalence between Goerss’ model category of simplicial coalgebras and Getzler–Goerss’ model category