  The construction of the formal ball model for metric spaces due to Edalat and
Heckmann was generalized to ${\sf Q}$-categories by Kostanek and Waszkiewicz.
This paper concerns the influence of the structure of the quantale ${\sf Q}$ on
the connection between Yoneda completeness of ${\sf Q}$-categories and directed
completeness of their sets of formal balls. In the case that ${\sf Q}$ is the
interval $[0,1]$ equipped with a continuous t-norm $\&$, it is shown that in
order that Yoneda completeness of each ${\sf Q}$-category be equivalent to
directed completeness of its set of formal balls, a necessary and sufficient
condition is that the t-norm $\&$ is Archimedean.
