 Coseparator

A coseparator $S$ in a category distinguishes parallel arrows by postcomposition: if $u\ne v:X\to B$, some $t:B\to S$ satisfies $tu\ne tv$. Equivalently, the contravariant functor $\mathcal{C}(-,S)$ is faithful. In a complete category that is a locally small category, the evaluation arrow $B\to {\prod }_{t\in \mathcal{C}(B,S)}S$ is a monomorphism.