Ordered Locales
Fuente:
arXiv
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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2023
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| _version_ | 1866910486357868544 |
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| author | Heunen, Chris van der Schaaf, Nesta |
| author_facet | Heunen, Chris van der Schaaf, Nesta |
| contents | We extend the Stone duality between topological spaces and locales to include order: there is an adjunction between the category of preordered topological spaces satisfying the so-called open cone condition, and the newly defined category of ordered locales. The adjunction restricts to an equivalence of categories between spatial ordered locales and sober $T_0$-ordered spaces with open cones. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2303_03813 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Ordered Locales Heunen, Chris van der Schaaf, Nesta Category Theory General Topology We extend the Stone duality between topological spaces and locales to include order: there is an adjunction between the category of preordered topological spaces satisfying the so-called open cone condition, and the newly defined category of ordered locales. The adjunction restricts to an equivalence of categories between spatial ordered locales and sober $T_0$-ordered spaces with open cones. |
| title | Ordered Locales |
| topic | Category Theory General Topology |
| url | https://arxiv.org/abs/2303.03813 |