A transitive relation is equivalently:[1]
- A non-unital $\mathbb {E}_{1}$-monoid in $\webleft (\mathrm{N}_{\bullet }\webleft (\mathbf{Rel}\webleft (A,A\webright )\webright ),\mathbin {\diamond }\webright )$.
- A non-unital monoid in $\webleft (\mathbf{Rel}\webleft (A,A\webright ),\mathbin {\diamond }\webright )$.
