Monoidal category action
In algebra, an action of a monoidal category on a category is a functor
such that there are natural isomorphisms and, which satisfy the coherence conditions analogous to those in. is said to act on.
Any monoidal category is a monoid object in [Category of small categories|] with the monoidal product being the category product. This means that equipped with an -action is exactly a module over a monoid in.
For example, acts on itself via the monoid operation.