Functor preserving pushouts
1. Definition
Let \(\mathcal{C}, \mathcal{D}\) be categories and \(\mathcal{F}: \mathcal{C} \rightarrow \mathcal{D}\) a functor. Then \(\mathcal{F}\) is said to preserve pushouts, if every pushout \(P\) is preserved under \(\mathcal{F}\)