Conditions de Kan sur les nerfs des ω-catégories

2021/02/08 by Félix Loubaton, Loubaton, Félix
Mathematics · Medicine · #Algebraic structures and combinatorial models #Category Theory (math.CT) #FOS: Mathematics #Homotopy and Cohomology in Algebraic Topology #Intracranial Aneurysms: Treatment and Complications

paper · pdf · doi:10.48550/arxiv.2102.04281

openalex publication_date 2021/02/08 · openalex created_date 2022/07/22 · openalex updated_date 2026/07/28

Abstract

We show that the Street nerve of a strict ω-category C is a Kan complex (respectively a quasi-category) if and only if the n-cells of C for n≥ 1 (respectively n> 1) are weakly invertible. Moreover, we equip N(C) with a structure of saturated complicial set where the n-simplices correspond to morphisms from the n^th oriental to C sending the unique non-trivial n-cell of the domain to a weakly invertible cell of C.

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