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# preadditive functor

###### Definition 0.1.

A functor between two preadditive categories $\mathcal{\mathcal{A}_{P}}$ and $\mathcal{\mathcal{A}^{{\prime}}_{P}}$ 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 $F(f+g)=F(f)+F(g)$.

Keywords:

pre (additive) functors of preadditive categories

Related:

AdditiveFunctor, PreadditiveCategory, GrothendieckCategory,LocalGrothendieckCategory, CategoryOfAdditiveFractions

Type of Math Object:

Definition

Major Section:

Reference

Groups audience:

## Mathematics Subject Classification

18E05*no label found*18-00

*no label found*

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