The associator of $\mathsf{Rel}$ is the natural isomorphism
\[ \alpha ^{\mathsf{Rel}}\colon {\times }\circ {\webleft ({\webleft (\times \webright )}\times {\mathsf{id}}\webright )}\mathbin {\overset {\mathord {\sim }}{\Longrightarrow }}{\times }\circ {\webleft ({\mathsf{id}}\times {\webleft (\times \webright )}\webright )}\circ {\mathbf{\alpha }^{\mathsf{Cats}}_{\mathsf{Rel},\mathsf{Rel},\mathsf{Rel}}}\mathrlap {,} \]
as in the diagram
whose component
\[ \alpha ^{\mathsf{Rel}}_{A,B,C}\colon \webleft (A\times B\webright )\times C\mathrel {\rightarrow \kern -9.5pt\mathrlap {|}\kern 6pt}A\times \webleft (B\times C\webright ) \]
at $A,B,C\in \text{Obj}\webleft (\mathsf{Rel}\webright )$ is the relation defined by declaring
\[ \webleft (\webleft (a,b\webright ),c\webright ) \sim _{\alpha ^{\mathsf{Rel}}_{A,B,C}} \webleft (a',\webleft (b',c'\webright )\webright ) \]
iff $a=a'$, $b=b'$, and $c=c'$.
