2018/08/24 by Sina Hazratpour, Hazratpour, Sina, Steven Vickers +1
Mathematics · #03G30 #18C10 #18D05 #18D30 #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.1808.08291
openalex publication_date 2018/08/24 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Suppose an extension map U\colon \mathbbT1 → \mathbbT0 in the 2-category \mathfrakCon of contexts for arithmetic universes satisfies a Chevalley criterion for being an (op)fibration in \mathfrakCon. If M is a model of \mathbbT0 in an elementary topos S with nno, then the classifier p\colonS[\mathbbT1/M]\toS satisfies Johnstone's criterion for being an (op)fibration in the 2-category E\mathfrakTop of elementary toposes (with nno) and geometric morphisms. Along the way, we provide a convenient reformulation of Johnstone's criterion.