Title of article
Formal balls of Q-categories
Author/Authors
Yang ، Xianbo School of Mathematics - Sichuan University , Zhang ، Dexue School of Mathematics - Sichuan University
From page
1
To page
18
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.
Keywords
Q , category , formal ball , continuous t , norm , quantale
Journal title
Categories and General Algebraic Structures with Applications
Journal title
Categories and General Algebraic Structures with Applications
Record number
2737272
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