additive functor and zero morphism
1. Proposition
Let \(\mathcal{A}, \mathcal{B}\) be additive categories and \(\mathcal{F}: \mathcal{A} \rightarrow \mathcal{B}\) be an additive functor Then for \(A,B \in \mathrm{Ob}(\mathcal{A})\) and the zero morphism \(0: A \rightarrow B\) it follows, that
\begin{align*} \mathcal{F}(0) = 0 \end{align*}