2024/03/22 by Ivan Di Liberti, Morgan Rogers, Di Liberti, Ivan +1
Mathematics · #03C75 #03G30 #18B25 #18C50 #18F10 #18F70 #Advanced Topology and Set Theory #Algebraic Geometry (math.AG) #Algebraic Geometry and Number Theory #Category Theory (math.CT) #FOS: Mathematics #Homotopy and Cohomology in Algebraic Topology #Logic (math.LO)
paper · pdf · doi:10.48550/arxiv.2403.15338
openalex publication_date 2024/03/22 · openalex created_date 2024/03/26 · openalex updated_date 2026/07/28
We extend Deligne's original argument showing that locally coherent topoi have enough points, clarified using collage diagrams. We show that our refinement of Deligne's technique can be adapted to recover every existing result of this kind, including the most recent results about κ-coherent κ-topoi. Our presentation allows us to relax the cardinality assumptions typically imposed on the sites involved. We show that a larger class of locally finitely presentable toposes have enough points and that a closed subtopos of a topos with enough points has enough points.