2025/11/13 by Soichiro Fujii, Fujii, Soichiro, Keisuke Hoshino +3
Mathematics · #18N20 #18N30 #18N40 #18N65 #Advanced Topology and Set Theory #Algebraic structures and combinatorial models #Category Theory (math.CT) #FOS: Mathematics #Homotopy and Cohomology in Algebraic Topology
paper · pdf · doi:10.48550/arxiv.2511.09849
openalex publication_date 2025/11/13 · openalex created_date 2025/11/15 · openalex updated_date 2026/07/28
We study ω-equifibrations between weak ω-categories in the sense of Batanin--Leinster. We define ω-equifibrations as a natural weak ω-categorical analogue of isofibrations between categories, and show that they can be characterised via the right lifting property with respect to a suitable set J of strict ω-functors. The definition of J involves the construction of a certain weak ω-category E1 which, roughly speaking, is freely generated by an equivalence 1-cell in a ``coherent'' manner. We show that the strict version of E1 coincides with Ozornova and Rovelli's coherent walking ω-equivalence \widehatωE. The ω-equifibrations between strict ω-categories coincide with the fibrations in the folk model structure.