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arXiv · 2207.08324

Formal balls of ${\sf Q}$-categories

Xianbo Yang·Dexue Zhang
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Abstract

The construction of the formal ball model for metric spaces due to Edalat and Heckmann was generalized to ${\sf Q}$-categories by Kostanek and Waszkiewicz. This paper concerns the influence of the structure of the quantale ${\sf Q}$ on the connection between Yoneda completeness of ${\sf Q}$-categories and directed completeness of their sets of formal balls. In the case that ${\sf Q}$ is the interval $[0,1]$ equipped with a continuous t-norm $\&$, it is shown that in order that Yoneda completeness of each ${\sf Q}$-category be equivalent to directed completeness of its set of formal balls, a necessary and sufficient condition is that the t-norm $\&$ is Archimedean.

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Xianbo Yang, Dexue Zhang. 2022-10-05. Formal balls of ${\sf Q}$-categories. https://arxiv.org/abs/2207.08324

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