preadditive functor

Definition 0.1   A functor between two preadditive categories $ \mathcal{\mathcal A_P}$ and $ \mathcal{\mathcal A'_P}$ is called a (pre) additive (or preadditive) functor, if for any pair of morphisms $ f, g \in Hom_{\mathcal{\mathcal A_P}}(X,Y)$ one has that $ F(f + g) = F(f) + F(g)$ .



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