21 citations · 69 across the 17 of their papers we have counts for
9 papers · 1 filter
Formal balls of -categories
Xianbo Yang, Dexue Zhang
The construction of the formal ball model for metric spaces due to Edalat and Heckmann was generalized to -categories by Kostanek and Waszkiewicz. This paper concerns the…
The double contravariant powerset monad in the Goguen category of fuzzy sets
Sijia Lu, Dexue Zhang
A monad is constructed in the Goguen category of fuzzy sets valued in a unital quantale, which is an analog of the double contravariant powerset monad in the category of sets. With…
The saturated prefilter monad
Hongliang Lai, Dexue Zhang, Gao Zhang
This paper considers some extensions of the notion of filter to the quantale-valued context, including saturated prefilter, -filter and bounded saturated prefilter. The quest…
Completely distributive enriched categories are not always continuous
Hongliang Lai, Dexue Zhang
In contrast to the fact that every completely distributive lattice is necessarily continuous in the sense of Scott, it is shown that complete distributivity of a category enriched…
Quantale-valued dissimilarity
Hongliang Lai, Lili Shen, Yuanye Tao +1
Inspired by the theory of apartness relations of Scott, we establish a positive theory of dissimilarity valued in an involutive quantale without the aid of negation. I…
Yoneda completeness and flat completeness of ordered fuzzy sets
Wei Li, Hongliang Lai, Dexue Zhang
This paper studies Yoneda completeness and flat completeness of ordered fuzzy sets valued in the quantale obtained by endowing the unit interval with a continuous triangular norm.…