Additive Categories
In mathematics, specifically in category theory, an additive category is a preadditive category C such that all finite collections of objects A1, … , An of C have a biproduct A1 ⊕ ⋯ ⊕ An in C.
A category C is preadditive if all its hom-sets are Abelian groups and composition of morphisms is bilinear; in other words, C is enriched over the monoidal category of Abelian groups. A biproduct in a preadditive category is both a finitary product and a finitary coproduct.
Read more about Additive Categories: Definition, Examples, Internal Characterisation of The Addition Law, Matrix Representation of Morphisms, Additive Functors, Special Cases
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