A reflexive relation is equivalently:1
- An $\mathbb {E}_{0}$-monoid in $\webleft (\mathrm{N}_{\bullet }\webleft (\mathbf{Rel}\webleft (A,A\webright )\webright ),\chi _{A}\webright )$;
- A pointed object in $\webleft (\mathbf{Rel}\webleft (A,A\webright ),\chi _{A}\webright )$.
1Note that since $\mathbf{Rel}\webleft (A,A\webright )$ is posetal, reflexivity is a property of a relation, rather than extra structure.
