An additive functor between preadditive categories is a functor 
that induces a group
homomorphism from each morphism group 
to 
. Equivalently, 
for every pair of morphisms 
(Stacks Project Authors 2026).
Additive Functor
See also
Additive Category, Functor, Preadditive CategoryExplore with Wolfram|Alpha
References
The Stacks Project Authors. "Preadditive and Additive Categories." Definition 12.3.1 in The Stacks Project, Tag 00ZY, 2026. https://stacks.math.columbia.edu/tag/00ZY.Referenced on Wolfram|Alpha
Additive FunctorCite this as:
Weisstein, Eric W. "Additive Functor." From MathWorld--A Wolfram Resource. https://mathworld.wolfram.com/AdditiveFunctor.html