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 -groupoids exists, then it satisfies the homotopy hypothesis, i.e. the associated -category is equivalent to that of homotopy -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.
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}
}