An additive category is a category for which the morphism sets have the structure of Abelian groups. It satisfies some, but not all the properties of an Abelian category.
Additive Category
See also
Abelian Category, Abelian GroupThis entry contributed by John Renze
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Renze, John. "Additive Category." From MathWorld--A Wolfram Web Resource, created by Eric W. Weisstein. https://mathworld.wolfram.com/AdditiveCategory.html