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On the homotopy hypothesis for 3-groupoids

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Simon Henry and Edoardo Lanari

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.

Keywords:
Homotopy hypothesis, Grothendieck's ∞-groupoids, model categories

2020 MSC:
18N20, 18N40, 18M90, 55U35

*Theory and Applications of Categories,*
Vol. 39, 2023,
No. 26, pp 735-768.

Published 2023-08-25.

http://www.tac.mta.ca/tac/volumes/39/26/39-26.pdf

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