• The relation $R\colon A\mathrel {\rightarrow \kern -9.5pt\mathrlap {|}\kern 6pt}B$ is an isomorphism in $\mathrm{Rel}$, i.e.:
    • There exists a relation $R^{-1}\colon B\mathrel {\rightarrow \kern -9.5pt\mathrlap {|}\kern 6pt}A$ from $B$ to $A$ such that we have
      \begin{align*} R^{-1}\mathbin {\diamond }R & = \chi _{A},\\ R\mathbin {\diamond }R^{-1} & = \chi _{B}. \end{align*}


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