English

Model category structures \`a la Thomason on 2-Cat

Algebraic Topology 2020-09-07 v1 Category Theory

Abstract

In his paper "Th\'eories homotopiques des 2-cat\'egories", Jonathan Chiche studies homotopy theories on 2-Cat, the category of small strict 2-categories, given by classes of weak equivalences which he calls basic localizers of 2-Cat. These basic localizers of 2-Cat are a 2-categorical generalization of the notion of a basic localizer introduced by Grothendieck in "Pursuing stacks". In this paper, we deduce from the results of Jonathan Chiche and results we have obtained with Georges Maltsiniotis that for essentially every basic localizer W of 2-Cat, there exists a model category structure \`a la Thomason on 2-Cat whose weak equivalences are given by W. We show that these model category structures model exactly combinatorial left Bousfield localization of the classical homotopy theory of simplicial sets.

Keywords

Cite

@article{arxiv.1607.03644,
  title  = {Model category structures \`a la Thomason on 2-Cat},
  author = {Dimitri Ara},
  journal= {arXiv preprint arXiv:1607.03644},
  year   = {2020}
}

Comments

21 pages, in French, was previously an appendix to arXiv:1309.0191, journal version

R2 v1 2026-06-22T14:53:15.181Z