Cartesian closedness of the category of real-valued sets, I
Fuente:
arXiv
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| Autori principali: | , |
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| Natura: | Preprint |
| Pubblicazione: |
2025
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| _version_ | 1866914264623611904 |
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| author | Shen, Lili Zhang, Jian |
| author_facet | Shen, Lili Zhang, Jian |
| contents | Let $[0,1]_*$ be the unit interval $[0,1]$ equipped with a continuous t-norm $*$. It is shown that the category of $[0,1]_*$-sets is cartesian closed if, and only if, $*$ is the minimum t-norm on $[0,1]$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2510_12108 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Cartesian closedness of the category of real-valued sets, I Shen, Lili Zhang, Jian Category Theory 03E72, 18D15, 18F75 Let $[0,1]_*$ be the unit interval $[0,1]$ equipped with a continuous t-norm $*$. It is shown that the category of $[0,1]_*$-sets is cartesian closed if, and only if, $*$ is the minimum t-norm on $[0,1]$. |
| title | Cartesian closedness of the category of real-valued sets, I |
| topic | Category Theory 03E72, 18D15, 18F75 |
| url | https://arxiv.org/abs/2510.12108 |