left adjoint as right exact functor

Let \(\mathcal{C}, \mathcal{D}\) be finitely cocomplete categories and \(\mathcal{F}: \mathcal{C} \rightarrow \mathcal{D}\) a functor which is a left adjoint. Then \(\mathcal{F}\) is right exact functor

corollary of:

• left adjoint preserves colimits