Diagonals between $\mathcal{Q}$-distributors

Abstract

For a small quantaloid $\mathcal{Q}$, it is shown that the category of $\mathcal{Q}$-distributors and diagonals is equivalent to a quotient category of the category of $\mathcal{Q}$-interior spaces and continuous $\mathcal{Q}$-distributors. Kan adjunctions induced by $\mathcal{Q}$-distributors play a crucial role in establishing this equivalence.

20 pages, final version

References in corpus (14)

• Categorical structures enriched in a quantaloid: categories, distributors and functors
• Categorical structures enriched in a quantaloid: tensored and cotensored categories
• Topological categories, quantaloids and Isbell adjunctions
• Fuzzy Galois connections on fuzzy sets
• $\mathcal{Q}$-closure spaces
• Yoneda completeness and flat completeness of ordered fuzzy sets
• Lax Distributive Laws for Topology, I
• Chu connections and back diagonals between $\mathcal{Q}$-distributors
• Towards probabilistic partial metric spaces: Diagonals between distance distributions
• Topology from enrichment: the curious case of partial metrics
• Limits and colimits of quantaloid-enriched categories and their distributors
• Quantale-valued dissimilarity
• Lax distributive laws for topology, II
• Regularity vs. constructive complete (co)distributivity