Shahid Beheshti UniversityCategories and General Algebraic Structures with Applications2345-585318120230201Formal balls of Q-categories11810291410.52547/cgasa.2022.102914ENXianbo YangSchool of Mathematics, Sichuan University, Chengdu, ChinaDexue ZhangSchool of Mathematics, Sichuan University, Chengdu, ChinaJournal Article20221202The 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.https://cgasa.sbu.ac.ir/article_102914_351656fec0984f81ec40c98cc66412ed.pdf