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preadditive functor (Definition)
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, and/or simply, 'additive', 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)$; (see also the definition of a preadditive category).



"preadditive functor" is owned by bci1. [ full author list (2) ]
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See Also: additive functor, preadditive category, Grothendieck category, local Grothendieck category, category of additive fractions

Keywords:  pre (additive) functors of preadditive categories
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Cross-references: preadditive category, morphisms, additive, categories, functor
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This is version 11 of preadditive functor, born on 2008-07-15, modified 2008-08-25.
Object id is 10791, canonical name is PreAdditiveFunctors.
Accessed 248 times total.

Classification:
AMS MSC: 18-00 (Category theory; homological algebra :: General reference works )
 18E05 (Category theory; homological algebra :: Abelian categories :: Preadditive, additive categories)
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