conservative functor

Let \(\mathcal{C}, \mathcal{D}\) be categories and \(F: \mathcal{C} \rightarrow \mathcal{D}\) a functor. \(F\) is a conservative functor, if for a morphism \(f \in \mathrm{Mor}(\mathcal{C})\), \(F(f) \in \mathrm{Mor}(\mathcal{D})\) being an isomorphism implies, that \(f\) is an isomorphism.