Subsubsection 6.2.3.6 (00K4): The Symmetry

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

whose component

\[ \sigma ^{\mathsf{Rel}}_{A,B} \colon A\times B \to B\times A \]

at $\webleft (A,B\webright )$ is defined by declaring

\[ \webleft (a,b\webright ) \sim _{\sigma ^{\mathsf{Rel}}_{A,B}} \webleft (b',a'\webright ) \]

iff $a=a'$ and $b=b'$.

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