15 citations · 89 across the 17 of their papers we have counts for
10 papers · 1 filter
Concept lattices of -relations via diagonal and back-diagonal categories
Hongliang Lai, Bo Pang
Let be a commutative unital quantale and $\QRel$ the ordered category of sets and -relations. We develop a categorical foundation for formal and property-oriented concept la…
Density in categorical topology via quantaloid-enriched categories
Hongliang Lai, Lili Shen
Based on Garner's discovery that topological categories are total categories enriched in a quantaloid, this paper presents a series of results related to initial and final density…
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…
Monads on Q-Cat and their lax extensions to Q-Dist
Hongliang Lai, Walter Tholen
For a small quantaloid , we consider 2-monads on the 2-category - and their lax extensions to the 2-category - of small…