Additive Category

In mathematics, specifically in category theory, an additive category is a preadditive category C such that all finite collections of objects A₁, … , A_n of C have a biproduct A₁ ⊕ ⋯ ⊕ A_n in C.

Recall that 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. Recall also that a biproduct in a preadditive category is both a finitary product and a finitary coproduct.