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