Monoidal category action
In algebra, an action of a monoidal category ( S , ⊗ , e ) {\displaystyle (S,\otimes ,e)} on a category X {\displaystyle X} is a functor ⋅ : S × X → X {\displaystyle \cdot :S\times X\to X} such that there are natural isomorphisms s ⋅ ( t ⋅ x ) ≃ ( s ⊗ t ) ⋅ x {\displaystyle s\cdot (t\cdot x)\simeq (s\otimes t)\cdot x} and e ⋅ x ≃ x {\displaystyle e\cdot x\simeq x} , which satisfy the coherence conditions analogous to those in S {\displaystyle S} . S {\displaystyle S} is said to act on X {\displaystyle X} .