2021/09/23 by Dominique Bourn, Bourn, Dominique
Mathematics · #08A30 #08B05 #18B25 #18C40 #18D30 #18E13 #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.2109.11381
openalex publication_date 2021/09/23 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
In a regular category \mathbb E, the direct image along a regular epimorphism f of a preorder is not a preorder in general. In Set, its best preorder approximation is then its cocartesian image above f. In a regular category, the existence of such a cocartesian image above f of a preorder S is actually equivalent to the existence of the supremum R[f]\vee S among the preorders. We investigate here some conditions ensuring the existence of these cocartesian images or equivalently of these suprema. They applied to two very dissimilar contexts: any topos \mathbb E with suprema of chains of subobjects or any n-permutable regular category.