The powerset monad on quantale-valued sets

Abstract

For a small involutive quantaloid $\mathcal{Q}$, it is shown that the category of separated complete $\mathcal{Q}$-categories and left adjoint $\mathcal{Q}$-functors is strictly monadic over the category of symmetric $\mathcal{Q}$-categories. In particular, the (covariant) powerset monad on the category of quantale-valued sets is precisely formulated.

arXiv comment17 pages, final version

References in corpus (6)

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• Categorical structures enriched in a quantaloid: tensored and cotensored categories
• Categories enriched over a quantaloid: Isbell adjunctions and Kan adjunctions
• Adjunctions in Quantaloid-enriched Categories
• Symmetry and Cauchy completion of quantaloid-enriched categories
• Quantale-valued dissimilarity