Subsubsection 5.2.2.5 (00K2): The Right Unitor

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The right unitor of $\mathsf{Rel}$ is the natural isomorphism

whose component

\[ \rho ^{\mathsf{Rel}}_{A} \colon A\times \mathbb {1}_{\mathsf{Rel}} \mathrel {\rightarrow \kern -9.5pt\mathrlap {|}\kern 6pt}A \]

at $A$ is defined by declaring

\[ \webleft (a,\star \webright ) \sim _{\rho ^{\mathsf{Rel}}_{A}} b \]

iff $a=b$.

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