functor preserving epimorphisms

Let \(\mathcal{C}, \mathcal{D}\) be categories and \(\mathcal{F}: \mathcal{C} \rightarrow \mathcal{D}\) be a functor. Then \(\mathcal{F}\) is said to be preserve epimorphisms, if for an epimorphism \(f \in \mathrm{Mor}(\mathcal{C})\)

\begin{align*} \mathcal{F}(f) \end{align*}

is also an epimorphism