Topoi with enough points

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 $\kappa$-...

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Bibliographic Details
Main Authors Di Liberti, Ivan, Rogers, Morgan
Format Journal Article
LanguageEnglish
Published 22.03.2024
Subjects
Mathematics - Algebraic Geometry
Mathematics - Category Theory
Mathematics - Logic
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Summary: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 $\kappa$-coherent $\kappa$-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.
DOI:10.48550/arxiv.2403.15338