Definition:Preadditive Category

Definition
A preadditive category is a monoidally enriched category over the monoidal category of abelian groups $\mathbf {A b}$.

That is, a category such that:
 * its hom sets are abelian groups

and where:
 * composition is bilinear.

Also see

 * Definition:Additive Category
 * Definition:Abelian Category