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arXiv · 2609.05929

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

Lili Shen·Jian Zhang
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Abstract

Let $[0,1]_*$ be the unit interval $[0,1]$ equipped with a left-continuous t-norm $*$. We prove that $[0,1]_*\text{-}\mathbf{Set}$ is cartesian closed if and only if $*$ is the minimum t-norm. This extends the classification for continuous t-norms established in the first part of this work to the whole left-continuous setting.

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Lili Shen, Jian Zhang. 2026-09-05. Cartesian closedness of the category of real-valued sets, II. https://arxiv.org/abs/2609.05929

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