TY - JOUR
ID - 102914
TI - Formal balls of Q-categories
JO - Categories and General Algebraic Structures with Applications
JA - CGASA
LA - en
SN - 2345-5853
AU - Yang, Xianbo
AU - Zhang, Dexue
AD - School of Mathematics, Sichuan University, Chengdu, China
Y1 - 2023
PY - 2023
VL - 18
IS - 1
SP - 1
EP - 18
KW - Q-category
KW - formal ball
KW - continuous t-norm
KW - quantale
DO - 10.52547/cgasa.2022.102914
N2 - 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.
UR - https://cgasa.sbu.ac.ir/article_102914.html
L1 - https://cgasa.sbu.ac.ir/article_102914_351656fec0984f81ec40c98cc66412ed.pdf
ER -