Monoidal category action

In algebra, an action of a monoidal category "S" on a category "X" is a functor
such that there are natural isomorphisms formula_2 and formula_3 and those natural isomorphism satisfy the coherence conditions analogous to those in "S". If there is such an action, "S" is said to act on "X".
For example, "S" acts on itself via the monoid operation ⊗.