饱和预滤单子
The saturated prefilter monad
摘要：
本文将滤子概念推广到量子值情形，包括饱和预滤子、$\top$ -滤子和有界饱和预滤子。问题是这些构造是否会在集合的集范畴上产生单子。结果表明，答案取决于Quantale的结构。具体地说，如果Quantale是配备有连续t-范数的单位区间，则这些构造产生单子当且仅当对应于该t-范数的蕴涵算子在对角线外的每一点处连续。
英文摘要：
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.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
