Rel, bicategory of relations, allegory
left and right euclidean;
extensional, well-founded relations.
A (binary) relation $\sim$ on a set $A$ is reflexive if every element of $A$ is related to itself:
In the language of the $2$-poset Rel of sets and relations, a relation $R: A \to A$ is reflexive if it contains the identity relation on $A$:
reflexive relation, irreflexive relation