Additive functors between preadditive categories generalize the concept of ring homomorphism, and ideals in additive categories can be defined as sets of morphisms closed under addition and under composition with arbitrary morphisms. Source: Internet
Additive functors If C and D are preadditive categories, then a functor F: C → D is additive if it too is enriched over the category Ab. Source: Internet
Additivity If C and D are preadditive categories and F : C ← D is an additive functor with a right adjoint G : C → D, then G is also an additive functor and the hom-set bijections : are, in fact, isomorphisms of abelian groups. Source: Internet
Further facts about kernels and cokernels in preadditive categories that are mainly useful in the context of pre-Abelian categories may be found under that subject. Source: Internet
An additive category is a preadditive category in which all finite biproduct exist. Source: Internet
Examples The most obvious example of a preadditive category is the category Ab itself. Source: Internet