arXiv subjects

Xiaoye Tang

Publications and source records attributed to Xiaoye Tang.

4 recordsLinked to original sources

arXiv2025

Completeness of quantaloid-enriched categories up to Morita equivalence

For a small quantaloid $\mathcal{Q}$, we introduce $\mathcal{M}$-(co)complete $\mathcal{Q}$-categories, i.e., (co)complete $\mathcal{Q}$-categories up to Morita equivalence, as Eilenberg--Moore algebras of the presheaf monad on the category of $\mathcal{Q}$-categories and left adjoint $\mathcal{Q}$-distributors, and characterize such $\mathcal{Q}$-categories through $\mathcal{M}$-(co)tensoredness and $\mathcal{M}$-conical (co)completeness.

math.CT↗

arXiv2025

Reducts of fuzzy contexts: Formal concept analysis vs. rough set theory

We postulate the intuitive idea of reducts of fuzzy contexts based on formal concept analysis and rough set theory. For a complete residuated lattice $L$, it is shown that reducts of $L$-contexts in formal concept analysis are interdefinable with reducts of $L$-contexts in rough set theory via negation if, and only if, $L$ satisfies the law of double negation.

cs.LO↗

arXiv2024

Quantale-valued maps and partial maps

Let $\mathsf{Q}$ be a commutative and unital quantale. By a $\mathsf{Q}$-map we mean a left adjoint in the quantaloid of sets and $\mathsf{Q}$-relations, and by a partial $\mathsf{Q}$-map we refer to a Kleisli morphism with respect to the maybe monad on the category $\mathsf{Q}\text{-}\mathbf{Map}$ of sets and $\mathsf{Q}$-maps. It is shown that every $\mathsf{Q}$-map is symmetric if and only if $\mathsf{Q}$ is weakly lean, and that every $\mathsf{Q}$-map is exactly a map in $\mathbf{Set}$ if and only $\mathsf{Q}$ is lean. Moreover, assuming the axiom of choice, it is shown that the category of sets and partial $\mathsf{Q}$-maps is monadic over $\mathsf{Q}\text{-}\mathbf{Map}$.

math.CT↗

arXiv2022

Isbell adjunctions and Kan adjunctions via quantale-enriched two-variable adjunctions

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 Kan adjunctions are precisely Isbell adjunctions constructed from suitable associated two-variable adjunctions. Representation theorems are established for fixed points of these adjunctions.

math.CT↗