论文标题
饱和的预滤器单元
The saturated prefilter monad
论文作者
论文摘要
本文考虑了过滤器概念到量化值的某些扩展，包括饱和的预滤器，$ \ top $ - 滤波器和有界的饱和预滤器。问题是这些结构是否引起了集合类别的单调。结果表明，答案取决于量化的结构。具体而言，如果量化是配备了连续T-norm的单位间隔，则这些构造在且仅当与对角线的每个点相对应的含义算子是连续的，并且仅当对应于该T-norm的含义是连续的。
This paper considers some extensions of the notion of filter to the quantale-valued context, including saturated prefilter, $\top$-filter and bounded saturated prefilter. The question is whether these constructions give rise to monads on the category of sets. It is shown that the answer depends on the structure of the quantale. Specifically, if the quantale is the unit interval equipped with a continuous t-norm, then these constructions give rise to monads if and only if the implication operator corresponding to that t-norm is continuous at each point off the diagonal.
