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On the homotopy hypothesis for 3-groupoids
- 1.0575355 - MÚ 2024 RIV CA eng J - Journal Article
Henry, S. - Lanari, Edoardo
On the homotopy hypothesis for 3-groupoids.
Theory and Applications of Categories. Roč. 39, č. 26 (2023), s. 735-768. ISSN 1201-561X
Grant - others:AV ČR(CZ) AP1801
Program: Akademická prémie - Praemium Academiae
Institutional support: RVO:67985840
Keywords : Grothendieck’s ∞-groupoids * homotopy hypothesis * model categories
OECD category: Pure mathematics
Impact factor: 0.5, year: 2022
Method of publishing: Open access
http://www.tac.mta.ca/tac/volumes/39/26/39-26.pdf
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.
Permanent Link: https://hdl.handle.net/11104/0345140
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