论文标题
$ {\ sf Q} $的正式球类别
Formal balls of ${\sf Q}$-categories
论文作者
论文摘要
由Kostanek和Waszkiewicz概括了由于Edalat和Heckmann引起的正式球模型的构建为$ {\ sf Q} $ - 类别。本文涉及量子$ {\ sf q} $的结构对$ {\ sf q} $的yoneda完整性之间的连接的影响 - 类别与他们的正式球的指示完整性。如果$ {\ sf q} $是配备了连续t-norm $ \＆$的间隔$ [0,1] $，则表明，为了使每个$ {\ sf q} $ - 类别的yoneda的完整性相当于其正式球的指向完整性，以置于正式的状态，并充分的条件，即them $;
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.
