proposition: Lemma actegory_from_precomp_CAT_laws : actegory_laws Mon_endo actegory_from_precomp_CAT_data.
proof: 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.
imports: UniMath.Foundations.PartD UniMath.MoreFoundations.All UniMath.CategoryTheory.Core.Categories UniMath.CategoryTheory.Core.Functors UniMath.CategoryTheory.Core.NaturalTransformations UniMath.CategoryTheory.FunctorCategory UniMath.CategoryTheory.BicatOfCatsElementary UniMath.CategoryTheory.whiskering UniMath.CategoryTheory.Monoidal.WhiskeredBifunctors UniMath.CategoryTheory.Monoidal.Categories UniMath.CategoryTheory.Monoidal.Examples.EndofunctorsMonoidalElementary UniMath.CategoryTheory.Actegories.Actegories UniMath.CategoryTheory.Actegories.ConstructionOfActegories UniMath.CategoryTheory.Actegories.MorphismsOfActegories UniMath.CategoryTheory.Limits.BinCoproducts UniMath.CategoryTheory.Limits.Coproducts UniMath.CategoryTheory.Actegories.CoproductsInActegories