2018/09/21 by Edoardo Lanari, Lanari, Edoardo
Mathematics · Medicine · #Algebraic structures and combinatorial models #Category Theory (math.CT) #FOS: Mathematics #Homotopy and Cohomology in Algebraic Topology #Intracranial Aneurysms: Treatment and Complications #math.CT
paper · pdf · doi:10.48550/arxiv.1809.07923
arxiv created 2018/09/21 · openalex publication_date 2018/09/21 · arxiv updated 2018/09/24 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
In this paper we apply some tools developed in our previous work on Grothendieck ∞-groupoids to the finite-dimensional case of weak 3-groupoids. We obtain a semi-model structure on the category of Grothendieck 3-groupoids of suitable type, thanks to the construction of an endofunctor ℙ that has enough structure to behave like a path object. This makes use of a recognition principle we prove here that characterizes globular theories whose models can be viewed as Grothendieck n-groupoids (for 0≤ n ≤ ∞). Finally, we prove that the obstruction in arbitrary dimension (possibly infinite) only resides in the construction of (slightly less than) a path object on a suitable category of Grothendieck (weak) n-categories with weak inverses. This also gives a sufficient condition for endowing an n-groupoid à la Batanin with the structure of a Grothendieck n-groupoid.