Subsubsection 5.2.2.4 (00K0): The Left Unitor

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

whose component

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

at $A$ is defined by declaring

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

iff $a=b$.

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