In detail, a relation $R$ on $A$ is transitive if we have an inclusion
\[ \mu _{R}\colon R\mathbin {\diamond }R\subset R \]
of relations in $\mathbf{Rel}\webleft (A,A\webright )$, i.e. if, for each $a,c\in A$, the following condition is satisfied:
- If there exists some $b\in A$ such that $a\sim _{R}b$ and $b\sim _{R}c$, then $a\sim _{R}c$.
