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In mathematics, specifically in category theory, an additive category is a preadditive category C such that any finitely many objects A1,...,An of C have a biproduct A1 ? ? ? An in C. (Recall that a category C is preadditive if all its morphism sets are Abelian groups and morphism composition is bilinear, i.e. if C is enriched over the monoidal category of Abelian groups; and recall 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. The original example of an additive category is the category Ab of Abelian groups with group homomorphisms. Ab is preadditive because it is a closed monoidal category, and the biproduct in Ab is the finite direct sum.
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Additive Category Subcategories
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