Topoi with enough points
Fuente:
arXiv
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| Hauptverfasser: | , |
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| Format: | Preprint |
| Veröffentlicht: |
2024
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| _version_ | 1866929410109603840 |
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| author | Di Liberti, Ivan Rogers, Morgan |
| author_facet | Di Liberti, Ivan Rogers, Morgan |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2403_15338 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Topoi with enough points Di Liberti, Ivan Rogers, Morgan Category Theory Algebraic Geometry Logic 03G30, 03C75, 18B25, 18C50, 18F10, 18F70 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. |
| title | Topoi with enough points |
| topic | Category Theory Algebraic Geometry Logic 03G30, 03C75, 18B25, 18C50, 18F10, 18F70 |
| url | https://arxiv.org/abs/2403.15338 |