Cartesian closed and stable subconstructs of [0,1]-Cat
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arXiv
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| Format: | Preprint |
| Published: |
2024
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| _version_ | 1866911987027410944 |
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| author | Lai, Hongliang Luo, Qingzhu |
| author_facet | Lai, Hongliang Luo, Qingzhu |
| contents | Let $\&$ be a continuous triangular norm on the unit interval $[0,1]$ and $\mathbf{A}$ be a cartesian closed and stable subconstruct of the category consisting of all real-enriched categories. Firstly, it is shown that the category $\mathbf{A}$ is cartesian closed if and only if it is determined by a suitable subset $S\subseteq{M^2}$ of $[0,1]^2$, where $M$ is the set of all elements $x$ in $[0,1]$ such that $x\& x$ is idempotent. Secondly, it is shown that all Yoneda complete real-enriched categories valued in the set $M$ and Yoneda continuous $[0,1]$-functors form a cartesian closed category. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2401_01071 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Cartesian closed and stable subconstructs of [0,1]-Cat Lai, Hongliang Luo, Qingzhu Category Theory Let $\&$ be a continuous triangular norm on the unit interval $[0,1]$ and $\mathbf{A}$ be a cartesian closed and stable subconstruct of the category consisting of all real-enriched categories. Firstly, it is shown that the category $\mathbf{A}$ is cartesian closed if and only if it is determined by a suitable subset $S\subseteq{M^2}$ of $[0,1]^2$, where $M$ is the set of all elements $x$ in $[0,1]$ such that $x\& x$ is idempotent. Secondly, it is shown that all Yoneda complete real-enriched categories valued in the set $M$ and Yoneda continuous $[0,1]$-functors form a cartesian closed category. |
| title | Cartesian closed and stable subconstructs of [0,1]-Cat |
| topic | Category Theory |
| url | https://arxiv.org/abs/2401.01071 |