nLab additive monad

Idea

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.

Related concepts

• strong monad