On the Cartesian closedness of [0,1]-Cat and some of its subcategories
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arXiv
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| Hauptverfasser: | , |
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| Format: | Preprint |
| Veröffentlicht: |
2025
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| _version_ | 1866914275880075264 |
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| author | Lai, Hongliang Luo, Qingzhu |
| author_facet | Lai, Hongliang Luo, Qingzhu |
| contents | We describe all left continuous triangular norms for which the category [0,1]-Cat of real-enriched categories and functors is cartesian closed. We furthermore show that the cartesian closedness of [0,1]-Cat is equivalent to the cartesian closedness of either (and thus all) of the following subcategories: the full subcategory of Cauchy complete [0,1]-categories; the subcategory of Yoneda complete [0,1]-categories and Yoneda continuous [0,1]-functors; the full subcategory of Smyth complete [0,1]-categories; and the full subcategory of finite [0,1]-categories. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2501_09243 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | On the Cartesian closedness of [0,1]-Cat and some of its subcategories Lai, Hongliang Luo, Qingzhu Category Theory We describe all left continuous triangular norms for which the category [0,1]-Cat of real-enriched categories and functors is cartesian closed. We furthermore show that the cartesian closedness of [0,1]-Cat is equivalent to the cartesian closedness of either (and thus all) of the following subcategories: the full subcategory of Cauchy complete [0,1]-categories; the subcategory of Yoneda complete [0,1]-categories and Yoneda continuous [0,1]-functors; the full subcategory of Smyth complete [0,1]-categories; and the full subcategory of finite [0,1]-categories. |
| title | On the Cartesian closedness of [0,1]-Cat and some of its subcategories |
| topic | Category Theory |
| url | https://arxiv.org/abs/2501.09243 |