On the homotopy hypothesis for 3-groupoids

0575355 - MÚ 2024 RIV CA eng J - Článek v odborném periodiku
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 ostatní: AV ČR(CZ) AP1801
Program: Akademická prémie - Praemium Academiae
Institucionální podpora: RVO:67985840
Klíčová slova: Grothendieck’s ∞-groupoids * homotopy hypothesis * model categories
Obor OECD: Pure mathematics
Impakt faktor: 0.5, rok: 2022
Způsob publikování: 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.
Trvalý link: https://hdl.handle.net/11104/0345140