Could not include enriched category theory - contents
additive and abelian categories
(AB1) pre-abelian category
(AB2) abelian category
(AB5) Grothendieck category
left/right exact functor
A monad $\mathbf{G}=(G,\mu,\eta)$ on an additive category $A$ is additive if its underlying endofunctor $G:A\to A$ is an additive functor. One defines an additive comonad in the same vein.
Note that every additive category is Ab-enriched, and an additive monad is then the same as an Ab-enriched monad.