Poset-enriched pretoposes and compact ordered spaces
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arXiv
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| Format: | Preprint |
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2025
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| _version_ | 1866913988954030080 |
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| author | Marquès, Jérémie Reggio, Luca |
| author_facet | Marquès, Jérémie Reggio, Luca |
| contents | We provide a characterisation of the category $\mathsf{KOrd}$ of Nachbin's compact ordered spaces as a poset-enriched category. Up to equivalence, $\mathsf{KOrd}$ is the only non-degenerate poset-enriched pretopos whose terminal object is a (discrete) generator and in which every object is covered by an order-filtral object. Order-filtral objects satisfy an appropriate form of compactness and separation. Throughout, we make extensive use of the internal language of poset-enriched pretoposes. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2508_09944 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Poset-enriched pretoposes and compact ordered spaces Marquès, Jérémie Reggio, Luca Category Theory Logic 18F60, 03G30, 18D20, 18E08 We provide a characterisation of the category $\mathsf{KOrd}$ of Nachbin's compact ordered spaces as a poset-enriched category. Up to equivalence, $\mathsf{KOrd}$ is the only non-degenerate poset-enriched pretopos whose terminal object is a (discrete) generator and in which every object is covered by an order-filtral object. Order-filtral objects satisfy an appropriate form of compactness and separation. Throughout, we make extensive use of the internal language of poset-enriched pretoposes. |
| title | Poset-enriched pretoposes and compact ordered spaces |
| topic | Category Theory Logic 18F60, 03G30, 18D20, 18E08 |
| url | https://arxiv.org/abs/2508.09944 |