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In mathematics, specifically in category theory, a pre-abelian category is an additive category that has all kernels and cokernels.
Spelled out in more detail, this means that a category C is pre-abelian if:
Note that the zero morphism in item 3 can be identified as the identity element of the hom-set Hom, which is an abelian group by item 1; or as the unique morphism A → 0 → B, where 0 is a zero object, guaranteed to exist by item 2.
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