proposition: Lemma lax_lineators_for_actegory_from_precomp_and_self_action_agree (F : functor (endocat c0) (endocat c0)) : lineator_lax (Mon_endo c0) (actegory_from_precomp c0 c0) (actegory_from_precomp c0 c0) F = lineator_lax (Mon_endo c0) (actegory_with_canonical_self_action (Mon_endo c0)) (actegory_with_canonical_self_action (Mon_endo c0)) F.
proof: Proof. assert (actegory_with_canonical_self_action (Mon_endo c0) = actegory_from_precomp c0 c0). { use subtypePath. { intro ; apply isaprop_actegory_laws. } apply idpath. } rewrite X. apply idpath. Qed.
imports: UniMath.Foundations.PartD UniMath.MoreFoundations.All UniMath.CategoryTheory.Core.Categories UniMath.CategoryTheory.Core.NaturalTransformations UniMath.CategoryTheory.FunctorCategory UniMath.CategoryTheory.Core.Functors UniMath.CategoryTheory.whiskering UniMath.CategoryTheory.Monoidal.WhiskeredBifunctors UniMath.CategoryTheory.Monoidal.Categories UniMath.Bicategories.MonoidalCategories.WhiskeredMonoidalFromBicategory UniMath.CategoryTheory.Actegories.Actegories UniMath.CategoryTheory.Actegories.ConstructionOfActegories UniMath.CategoryTheory.Actegories.MorphismsOfActegories UniMath.CategoryTheory.Monoidal.Examples.EndofunctorsMonoidalElementary UniMath.CategoryTheory.Actegories.Examples.ActionOfEndomorphismsInCATElementary UniMath.Bicategories.Core.Bicat UniMath.Bicategories.Core.BicategoryLaws UniMath.Bicategories.Core.Unitors UniMath.Bicategories.Core.Examples.BicatOfCats UniMath.CategoryTheory.Limits.BinCoproducts UniMath.CategoryTheory.Limits.Coproducts UniMath.CategoryTheory.Actegories.CoproductsInActegories