An additive category is a preadditive category that has a zero object and finite biproducts . In a preadditive
category , every hom-set is an Abelian
group and composition of morphisms
is bilinear . A biproduct
combines a finite categorical
product and coproduct with compatible structure
morphisms (Stacks Project Authors 2026).
Every Abelian category is additive, but an additive
category need not have all kernels and cokernels .
See also Abelian Category ,
Abelian Group ,
Additive Functor ,
Biproduct ,
Cokernel ,
Kernel ,
Preadditive
Category ,
Zero Object
Portions of this entry contributed by John
Renze
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References The Stacks Project Authors. "Preadditive and Additive Categories." §12.3 in The Stacks Project , Tags 00ZY and 0104, 2026.
https://stacks.math.columbia.edu/tag/09SE . Referenced
on Wolfram|Alpha Additive Category
Cite this as:
Weisstein, Eric W. , with contributions by John Renze . "Additive Category." From MathWorld https://mathworld.wolfram.com/AdditiveCategory.html
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