This page is about functors between linear categories. For other notions of “linear functor,” see Goodwillie calculus and polynomial functor.
There is a notion of map between linearly distributive categories called linearly distributive functor?, which is often shortened to “linear functor.”
A linear category is a category enriched over Vect, and similarly a linear functor is a functor enriched over $Vect$.
Unwrapping this a bit: given objects $x, y$ in a linear category $C$, the homset $hom(x,y)$ is equipped with the structure of a vector space, and a functor $F: C \to D$ between linear categories is said to be linear if the map
is linear for all $x,y \in C$.
Note that a linear functor between linear additive categories is automatically additive.
Last revised on May 6, 2022 at 14:34:26. See the history of this page for a list of all contributions to it.