Geodesic
On the homotopy hypothesis for 3-groupoids
Theory and applications of categories, Tome 39 (2023), pp. 735-768 Cet article a éte moissonné depuis la source Theory and Applications of Categories website

Voir la notice de l'article

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 
@article{TAC_2023_39_a25,
     author = {Simon Henry and Edoardo Lanari},
     title = {On the homotopy hypothesis for 3-groupoids},
     journal = {Theory and applications of categories},
     pages = {735--768},
     year = {2023},
     volume = {39},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/TAC_2023_39_a25/}
}
TY  - JOUR
AU  - Simon Henry
AU  - Edoardo Lanari
TI  - On the homotopy hypothesis for 3-groupoids
JO  - Theory and applications of categories
PY  - 2023
SP  - 735
EP  - 768
VL  - 39
UR  - http://geodesic.mathdoc.fr/item/TAC_2023_39_a25/
LA  - en
ID  - TAC_2023_39_a25
ER  - 
%0 Journal Article
%A Simon Henry
%A Edoardo Lanari
%T On the homotopy hypothesis for 3-groupoids
%J Theory and applications of categories
%D 2023
%P 735-768
%V 39
%U http://geodesic.mathdoc.fr/item/TAC_2023_39_a25/
%G en
%F TAC_2023_39_a25
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/