There is a prop Rel
Morphisms are relations \(R \subseteq \bar m \times \bar n\)
Composition with \(S \subseteq \bar n \times \bar p\) is
\(\{(i, k)\ |\ \exists (i, j) \in R \land \exists (j,k) \in S\}\)
Monoidal product is given by the coproduct, which amounts to placing the two relations side-by-side.