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arXiv · 2510.12108

Cartesian closedness of the category of real-valued sets, I

Lili Shen·Jian Zhang
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Abstract

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 $[0,1]$.

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Lili Shen, Jian Zhang. 2025-10-14. Cartesian closedness of the category of real-valued sets, I. https://doi.org/10.1016/j.fss.2026.109767

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