Groupoidal and truncated n-quasi-categories

2024/06/03 by Victor Brittes, Brittes, Victor
Decision Sciences · Mathematics · Medicine · #18N20 (Primary) 18N40 #18N55 #18N65 #55P15 (Secondary) #Algebraic Topology (math.AT) #Category Theory (math.CT) #FOS: Mathematics #Fuzzy and Soft Set Theory #Homotopy and Cohomology in Algebraic Topology #Intracranial Aneurysms: Treatment and Complications

paper · pdf · doi:10.48550/arxiv.2406.01490

openalex publication_date 2024/06/03 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We define groupoidal and (n+k)-truncated n-quasi-categories, which are the translation to the world of n-quasi-categories of groupoidal and truncated (∞, n)-Θ-spaces defined by Rezk. We show that these objects are the fibrant objects of model structures on the category of presheaves on Θ_n obtained by localisation of Ara's model structure for n-quasi-categories. Furthermore, we prove that the inclusion Δ→ Θ_n induces a Quillen equivalence between the model structure for groupoidal (resp. and n-truncated) n-quasi-categories and the Kan-Quillen model structure for spaces (resp. homotopy n-types) on simplicial sets. To get to these results, we also construct a cylinder object for n-quasi-categories.

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