On the homotopy hypothesis in dimension 3

2019/05/14 by Simon Henry, Henry, Simon, Edoardo Lanari +1
Mathematics · #18G30 #18G55 #55U10 #55U35 #Category Theory (math.CT) #FOS: Mathematics #math.CT #msc:18G30 #msc:18G55 #msc:55U10 #msc:55U35

paper · pdf · doi:10.48550/arxiv.1905.05625

arxiv created 2019/05/14 · arxiv updated 2019/05/15

Abstract

We show that if the canonical left semi-model structure on the category of Grothendieck n-groupoids exists, then it satisfies the homotopy hypothesis, i.e. the associated (∞,1)-category is equivalent to that of homotopy n-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.

Related

• Grothendieck's Homotopy Hypothesis
• A semi-model structure for Grothendieck weak 3-groupoids
• Algebraic models of homotopy types and the homotopy hypothesis
• Double categorical model of (∞,1)-categories
• Grothendieck ∞-groupoids, and still another definition of ∞-categories