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Stream: learning: questions

Topic: Coslice of Rel, with functions as objects

fosco (Dec 14 2020 at 08:26):

Has someone studied the following bicategory?

$\sf Rel$ is the bicategory of sets and relations; consider a fixed set $A$ and the coslice $A/{\sf Rel}$; now, $(A/{\sf Rel})_f$ is the full subcategory of $A/{\sf Rel}$ whose objects are the relations $A\to X$ that are also functions. Intuitively, it's like the coslice of $\sf Set$ over $A$, but morphisms are relations $R : X \to Y$ such that, for $u : A \to X, v : A \to Y$, one has $R\circ u=v$.