A linear functor over a field 
is a functor 
between categories whose
hom-sets are vector spaces
over 
and whose composition of morphisms is
bilinear, such that
the induced map on each hom-set
is a linear transformation. Equivalently,
for scalars 
and morphisms 
(Stacks Project Authors 2026).
Every linear functor is an additive functor.
Linear Functor
See also
Additive Functor, Functor, Hom-Set, Linear TransformationExplore with Wolfram|Alpha
References
The Stacks Project Authors. "Linear Categories." §22.24 in The Stacks Project, Definitions 22.24.1-22.24.2, Tag 09MI, 2026. https://stacks.math.columbia.edu/tag/09MI.Cite this as:
Weisstein, Eric W. "Linear Functor." From MathWorld--A Wolfram Resource. https://mathworld.wolfram.com/LinearFunctor.html