PlanetPhysics/Preadditive Functor

\newcommand{\sqdiagram}[9]{$$ \diagram #1 \rto^{#2} \dto_{#4}&

\eqno{\mbox{#9}}$$ }

A functor between two preadditive categories $$\mathcal{\A_P}$$ and $$\mathcal{\A'_P}$$ is called a (pre) additive (or preadditive) functor , if for any pair of morphisms $$f, g \in Hom_{\mathcal{\A_P}}(X,Y)$$ one has that $$F(f + g) = F(f) + F(g)$$.