Formal balls of Q-categories

Document Type : Research Paper

Authors

School of Mathematics, Sichuan University, Chengdu, China

Abstract

The construction of the formal ball model for metric spaces due to Edalat and Heckmann was generalized to Q-categories by Kostanek and Waszkiewicz, where Q is a commutative and unital quantale. This paper concerns the influence of the structure of the quantale Q on the connection between Yoneda completeness of Q-categories and directed completeness of their sets of formal balls. In the case that Q is the unit interval [0, 1] equipped with a continuous t-norm &, it is shown that in order that Yoneda completeness of each 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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References

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Categories and General Algebraic Structures with Applications
Volume 18, Issue 1
February 2023
Pages 1-18

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