English

On the homotopy hypothesis in dimension 3

Category Theory 2019-05-15 v1

Abstract

We show that if the canonical left semi-model structure on the category of Grothendieck nn-groupoids exists, then it satisfies the homotopy hypothesis, i.e. the associated (,1)(\infty,1)-category is equivalent to that of homotopy nn-types, thus generalizing a result of the first named author. As a corollary of the second named author's proof of the existence of the canonical left semi-model structure for Grothendieck 3-groupoids, we obtain a proof of the homotopy hypothesis for Grothendieck 3-groupoids.

Keywords

Cite

@article{arxiv.1905.05625,
  title  = {On the homotopy hypothesis in dimension 3},
  author = {Simon Henry and Edoardo Lanari},
  journal= {arXiv preprint arXiv:1905.05625},
  year   = {2019}
}
R2 v1 2026-06-23T09:06:06.622Z