Geodesic
On the homotopy hypothesis for 3-groupoids
Theory and applications of categories, Tome 39 (2023), pp. 735-768

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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.

Publié le :
Classification : 18N20, 18N40, 18M90, 55U35
Keywords: Homotopy hypothesis, Grothendieck's ∞-groupoids, model categories 
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     author = {Simon Henry and Edoardo Lanari},
     title = {On the homotopy hypothesis for 3-groupoids},
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Simon Henry; Edoardo Lanari. On the homotopy hypothesis for 3-groupoids. Theory and applications of categories, Tome 39 (2023), pp. 735-768. http://geodesic.mathdoc.fr/item/TAC_2023_39_a25/