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.