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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. (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 finite product and a finite coproduct.) Warning The term "additive category" is sometimes applied to any preadditive category, but Wikipedia does not follow this older practice. A category C is additive if
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