2025/09/30 by Clémence Chanavat, Chanavat, Clémence
Mathematics · Medicine · #18N30 #18N40 #18N65 #Algebraic Topology (math.AT) #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.2509.26563
openalex publication_date 2025/09/30 · openalex created_date 2025/10/19 · openalex updated_date 2026/07/28
We make strict n-categories even stricter by requiring they satisfy higher exchange laws governed by Hadzihasanovic's theory of regular directed complexes. We study the first properties of stricter n-categories, in particular, we define the Gray product, and prove stability under suspension, which is non-trivial. After reviewing and briefly expanding the theory diagrammatic sets and their associated model structures for (∞, n)-categories, we construct a folk model structure on stricter n-categories, show that the walking equivalence coincides with the stricter polygraph generated by the walking equivalence in diagrammatic sets, and finally, that the folk model structure on stricter n-categories is right transferred from the diagrammatic model structure along a nerve construction.