In mathematics, specifically in category theory, an additive category is a preadditive category C admitting all finitary biproducts. There are two equivalent...

used the term additive category for preadditive categories, but this page reserves this term for certain special preadditive categories (see § Special...

In mathematics, specifically in category theory, a pre-abelian category is an additive category that has all kernels and cokernels. Spelled out in more...

In Def. 1.2.6, it is required that an additive category have a zero object (empty biproduct). An additive category is preabelian if every morphism has both...

addition operation Additive set-function see Sigma additivity Additive category, a preadditive category with finite biproducts Additive inverse, an arithmetic...

preadditive category (or additive category, or abelian category), then D may be turned into a preadditive category (or additive category, or abelian category) in...

the quotient category C/~ will also be additive, and the quotient functor C → C/~ will be an additive functor. The concept of an additive congruence relation...

Such a category is called preadditive. If, furthermore, the category has all finite products and coproducts, it is called an additive category. If all...

homological algebra in mathematics, the homotopy category K(A) of chain complexes in an additive category A is a framework for working with chain homotopies...

full subcategory of Grp. Ab is an abelian category, but Grp is not. Indeed, Grp isn't even an additive category, because there is no natural way to define...