equivalences in/of -categories
model category, model -category
on chain complexes/model structure on cosimplicial abelian groups
related by the Dold-Kan correspondence
The notion of model -category (or model -category, for short) is the -categorification of that of model category.
Where the classical model structure on simplicial sets is an archetypical example of a model category, so simplicial -groupoids (“simplicial spaces”, bisimplicial sets) form an archetypical example of a model -category. In this example, a fundamental application of the theory says, for instance, that geometric realization preserves homotopy pullbacks of homotopy Kan fibrations (see there).
Aaron Mazel-Gee, Model ∞-categories I: some pleasant properties of the ∞-category of simplicial spaces (arXiv:1412.8411)
Aaron Mazel-Gee, Model ∞-categories II: Quillen adjunctions, New York Journal of Mathematics 27 (2021) 508-550. (arXiv:1510.04392, nyjm:27-21)
Aaron Mazel-Gee, Model ∞-categories III: the fundamental theorem, New York Journal of Mathematics 27 (2021) 551-599 (arXiv:1510.04777, nyjm:27-22)
Created on December 28, 2021 at 14:09:32. See the history of this page for a list of all contributions to it.