In mathematics, specifically in category theory, a **preadditive category** is a category that is enriched over the monoidal category of abelian groups. In other words, the category **C** is preadditive if every hom-set Hom(*A*,*B*) in **C** has the structure of an abelian group, and composition of morphisms is bilinear over the integers.

A preadditive category is also called an **Ab-category**, after the notation **Ab** for the category of abelian groups. Some authors have used the term *additive category* for preadditive categories, but Wikipedia follows the current trend of reserving this word for certain special preadditive categories (see special cases below).

Read more about Preadditive Category: Examples, Elementary Properties, Additive Functors, Biproducts, Kernels and Cokernels, Special Cases

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... A

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**Preadditive Category**- Special Cases

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