Let $A$ and $B$ be sets.
- The set of equivalence relations from $A$ to $B$ is the subset $\smash {\mathrm{Rel}^{\mathrm{eq}}\webleft (A,B\webright )}$ of $\mathrm{Rel}\webleft (A,B\webright )$ spanned by the equivalence relations.
- The poset of relations from $A$ to $B$ is is the subposet $\smash {\mathbf{Rel}^{\text{eq}}\webleft (A,B\webright )}$ of $\mathbf{Rel}\webleft (A,B\webright )$ spanned by the equivalence relations.
