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.

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

References

SHOWING 1-10 OF 36 REFERENCES

Coalgebras in symmetric monoidal categories of spectra

We show that all coalgebras over the sphere spectrum are cocommutative in the category of symmetric spectra, orthogonal spectra, $\Gamma$-spaces, $\mathcal{W}$-spaces and EKMM $\mathbb{S}$-modules.

Model Categories of Diagram Spectra

Working in the category T of based spaces, we give the basic theory of diagram spaces and diagram spectra. These are functorsD→T for a suitable small topological categoryD. WhenD is symmetric

A short course on $\infty$-categories

In this short survey we give a non-technical introduction to some main ideas of the theory of $\infty$-categories, hopefully facilitating the digestion of the foundational work of Joyal and Lurie.

A necessary and sufficient condition for induced model structures

A common technique for producing a new model category structure is to lift the fibrations and weak equivalences of an existing model structure along a right adjoint. Formally dual but technically

Rings, Modules, and Algebras in Stable Homotopy Theory

Introduction Prologue: the category of ${\mathbb L}$-spectra Structured ring and module spectra The homotopy theory of $R$-modules The algebraic theory of $R$-modules $R$-ring spectra and the

Dwyer-Kan localization revisited

A version of Dwyer-Kan localization in the context of infinity-categories and simplicial categories is presented. Some results of the classical papers by Dwyer and Kan on simplicial localization are

An algebraic model for commutative Hℤ–algebras

We show that the homotopy category of commutative algebra spectra over the Eilenberg-Mac Lane spectrum of the integers is equivalent to the homotopy category of E-infinity-monoids in unbounded chain

Parametrized spectra, multiplicative Thom spectra and the twisted Umkehr map

We introduce a general theory of parametrized objects in the setting of infinity categories. Although spaces and spectra parametrized over spaces are the most familiar examples, we establish our

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