separator of a category

Let \(\mathcal{C}\) be a category and \(\mathcal{G} \subseteq \mathcal{C}\) a collection of objects. Then \(\mathcal{G}\) is said to be a family of separators, if for \(f,g \in \mathrm{Hom}_{\mathcal{C}}(B,C)\) with \(f \neq g\) there exists a morphism \(h: A \rightarrow B\) such that

\begin{align*} f \circ h \neq g \circ h \end{align*}