2023/01/20 by Olivia Monjon, Monjon, Olivia, Jérôme Scherer +3
Mathematics · #18E13 #18E50 #18G45 #55P60 #55R70 #Algebraic Geometry and Number Theory #Algebraic Topology (math.AT) #Category Theory (math.CT) #Commutative Algebra and Its Applications #FOS: Mathematics #Homotopy and Cohomology in Algebraic Topology
paper · pdf · doi:10.48550/arxiv.2301.08672
openalex publication_date 2023/01/20 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
The correspondence between the concept of conditional flatness and admissibility in the sense of Galois appears in the context of localization functors in any semi-abelian category admitting a fiberwise localization. It is then natural to wonder what happens in the category of crossed modules where fiberwise localization is not always available. In this article, we establish an equivalence between conditional flatness and admissibility in the sense of Galois (for the class of regular epimorphisms) for regular-epi localization functors. We use this equivalence to prove that nullification functors are admissible for the class of regular epimorphisms, even if the kernels of their localization morphisms are not acyclic.