21 citations · 114 across the 17 of their papers we have counts for
17 papers
Injective symmetric quantaloid-enriched categories
Lili Shen, Hang Yang
We characterize injective objects, injective hulls and essential embeddings in the category of symmetric categories enriched in a small, integral and involutive quantaloid. In part…
Isbell adjunctions and Kan adjunctions via quantale-enriched two-variable adjunctions
Lili Shen, Xiaoye Tang
It is shown that every two-variable adjunction in categories enriched in a commutative quantale serves as a base for constructing Isbell adjunctions between functor categories, and…
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…
Diagonals between -distributors
Lili Shen
For a small quantaloid , it is shown that the category of -distributors and diagonals is equivalent to a quotient category of the category of $\mathcal{Q}…
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…
Multi-adjoint concept lattices via quantaloid-enriched categories
Hongliang Lai, Lili Shen
With quantaloids carefully constructed from multi-adjoint frames, it is shown that multi-adjoint concept lattices, multi-adjoint property-oriented concept lattices and multi-adjoin…
Towards probabilistic partial metric spaces: Diagonals between distance distributions
Jialiang He, Hongliang Lai, Lili Shen
The quantale of distance distributions is of fundamental importance for understanding probabilistic metric spaces as enriched categories. Motivated by the categorical interpretatio…
Fuzzy Galois connections on fuzzy sets
Javier Gutiérrez García, Hongliang Lai, Lili Shen
In fairly elementary terms this paper presents how the theory of preordered fuzzy sets, more precisely quantale-valued preorders on quantale-valued fuzzy sets, is established under…
Regularity vs. constructive complete (co)distributivity
Hongliang Lai, Lili Shen
It is well known that a relation between sets is regular if, and only if, is completely distributive (cd), where is the complete lattice consistin…
Lax distributive laws for topology, II
Hongliang Lai, Lili Shen, Walter Tholen
For a small quantaloid we consider four fundamental 2-monads on , given by the presheaf 2-monad and the copres…
Fixed points of adjoint functors enriched in a quantaloid
Hongliang Lai, Lili Shen
Representation theorems are established for fixed points of adjoint functors between categories enriched in a small quantaloid. In a very general setting these results set up a com…
-closure spaces
Lili Shen
For a small quantaloid , a -closure space is a small category enriched in equipped with a closure operator on its presheaf category. We inve…
Limits and colimits of quantaloid-enriched categories and their distributors
Lili Shen, Walter Tholen
It is shown that, for a small quantaloid Q, the category of small Q-categories and Q-functors is total and cototal, and so is the category of Q-distributors and Q-Chu transforms.
Chu connections and back diagonals between -distributors
Lili Shen, Yuanye Tao, Dexue Zhang
Chu connections and back diagonals are introduced as morphisms for distributors between categories enriched in a small quantaloid . These notions, meaningful for close…
Topological categories, quantaloids and Isbell adjunctions
Lili Shen, Walter Tholen
In fairly elementary terms this paper presents, and expands upon, a recent result by Garner by which the notion of topologicity of a concrete functor is subsumed under the concept…
Adjunctions in Quantaloid-enriched Categories
Lili Shen
This dissertation is devoted to a study of adjunctions concerning categories enriched over a quantaloid Q (or Q-categories for short), with the following types of adjunctions invol…
Categories enriched over a quantaloid: Isbell adjunctions and Kan adjunctions
Lili Shen, Dexue Zhang
Each distributor between categories enriched over a small quantaloid Q gives rise to two adjunctions between the categories of contravariant and covariant presheaves, and hence to…