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math.CT2025
Completeness of quantaloid-enriched categories up to Morita equivalence
Xiaoye Tang
For a small quantaloid , we introduce -(co)complete -categories, i.e., (co)complete -categories up to Morita equivalence, as Eil…
math.CT2024
Quantale-valued maps and partial maps
Lili Shen, Xiaoye Tang
Let be a commutative and unital quantale. By a -map we mean a left adjoint in the quantaloid of sets and -relations, and by a partial $\mathsf{…
math.CT2021
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…