Definition action_from_precomp_CAT_data : bifunctor_data [C, C] [C, D] [C, D]. Proof. use make_bifunctor_data. - intros v f. exact (functor_composite v f). - intros v f1 f2 β. exact (lwhisker_CAT v β). - intros f v1 v2 α. exact (rwhisker_CAT f α). Defined.
Require Import UniMath.Foundations.PartD. Require Import UniMath.MoreFoundations.All. Require Import UniMath.CategoryTheory.Core.Categories. Require Import UniMath.CategoryTheory.Core.Functors. Require Import UniMath.CategoryTheory.Core.NaturalTransformations. Require Import UniMath.CategoryTheory.FunctorCategory. Require Import UniMath.CategoryTheory.BicatOfCatsElementary. Require Import UniMath.CategoryTheory.whiskering. Require Import UniMath.CategoryTheory.Monoidal.WhiskeredBifunctors. Require Import UniMath.CategoryTheory.Monoidal.Categories. Require Import UniMath.CategoryTheory.Monoidal.Examples.EndofunctorsMonoidalElementary. Require Import UniMath.CategoryTheory.Actegories.Actegories. Require Import UniMath.CategoryTheory.Actegories.ConstructionOfActegories. Require Import UniMath.CategoryTheory.Actegories.MorphismsOfActegories. Require Import UniMath.CategoryTheory.Limits.BinCoproducts. Require Import UniMath.CategoryTheory.Limits.Coproducts. Require Import UniMath.CategoryTheory.Actegories.CoproductsInActegories. Section Action_From_Precomposition. End Action_From_Precomposition.