Given a binary relation$R$ from $X$ to $Y$, its opposite relation (or dual, inverse, converse, reverse, etc) is a relation $R^{op}$ from $Y$ to $X$ as follows:

$b$ is $R^{op}$-related to $a$ if and only if $a$ is $R$-related to $b$.

Note that $(R^{op})^{op} = R$.

The operation $op$ is part of the requirements for Rel to be an allegory.

Examples

If $f$ is a function thought as a functionalentire relation, then $f^{op}$ is also a function if and only if $f$ is a bijection; in that case, $f^{op}$ is the inverse of $f$.