%0 Journal Article
%T Formal balls of Q-categories
%J Categories and General Algebraic Structures with Applications
%I Shahid Beheshti University
%Z 2345-5853
%A Yang, Xianbo
%A Zhang, Dexue
%D 2023
%\ 02/01/2023
%V 18
%N 1
%P 1-18
%! Formal balls of Q-categories
%K Q-category
%K formal ball
%K continuous t-norm
%K quantale
%R 10.52547/cgasa.2022.102914
%X 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.
%U https://cgasa.sbu.ac.ir/article_102914_351656fec0984f81ec40c98cc66412ed.pdf