Lemma actegory_from_precomp_CAT_laws : actegory_laws Mon_endo actegory_from_precomp_CAT_data. Proof. split5. - exact action_from_precomp_CAT_laws. - split3. + intros f g β. apply vcomp_lunitor_CAT. + apply lunitor_linvunitor_CAT. + apply linvunitor_lunitor_CAT. - split4. + intros v w f f' β. apply lwhisker_lwhisker_rassociator_CAT. + intros v v' w f α. apply pathsinv0, rwhisker_rwhisker_alt_CAT. + intros v w w' f α. apply rwhisker_lwhisker_rassociator_CAT. + split. * apply rassociator_lassociator_CAT. * apply lassociator_rassociator_CAT. - intros v f. apply lunitor_lwhisker_CAT. - intros w v v' f. apply rassociator_rassociator_CAT. Qed.
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.