additive functor

An additive functor is an Ab-enriched functor

Let \(\mathcal{A}, \mathcal{B}\) be preadditive (?) categories and \(F: \mathcal{C} \rightarrow \mathcal{D}\) a functor. Then \(F\) is said to be additive, if for \(A,B \in \mathrm{Ob}(\mathcal{A})\)

\begin{align*} F: \mathrm{Hom}_{\mathcal{A}}(A,B) \rightarrow \mathrm{Hom}_{\mathcal{A}}(F(A), F(B)) \end{align*}

is a group homomorphism

see:

• additive functor and biproduct