The right unitor of $\mathsf{Rel}$ is the natural isomorphism
\[ \rho ^{\mathsf{Rel}}_{A} \colon A\times \mathbb {1}_{\mathsf{Rel}} \mathrel {\rightarrow \kern -9.5pt\mathrlap {|}\kern 6pt}A \]
at $A$ is defined by declaring
\[ \webleft (a,\star \webright ) \sim _{\rho ^{\mathsf{Rel}}_{A}} b \]
iff $a=b$.
