2024/06/19 by Soichiro Fujii, Fujii, Soichiro, Keisuke Hoshino +3
Mathematics · Medicine · #18N20 #18N40 #18N65 #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.2406.13240
openalex publication_date 2024/06/19 · openalex created_date 2024/06/22 · openalex updated_date 2026/07/28
We study ω-weak equivalences between weak ω-categories in the sense of Batanin-Leinster. Our ω-weak equivalences are strict ω-functors satisfying essential surjectivity in every dimension, and when restricted to those between strict ω-categories, they coincide with the weak equivalences in the model category of strict ω-categories defined by Lafont, Métayer, and Worytkiewicz. We show that the class of ω-weak equivalences has the 2-out-of-3 property. We also consider a generalisation of ω-weak equivalences, defined as weak ω-functors (in the sense of Garner) satisfying essential surjectivity, and show that this class also has the 2-out-of-3 property.