left exact functor preserves zero morphisms

Let \(\mathcal{C}, \mathcal{D}\) be a pointed, finitely complete categories and \(\mathcal{F}: \mathcal{C} \rightarrow \mathcal{D}\) a left exact functor Then \(\mathcal{F}\) preserves zero morphisms

corollary of:

1. terminal object as empty limit
2. terminal object as zero object in a pointed category
3. functor preserving zero morphism and preserving zero object