proposition: Lemma ab_strength_mor_from_signature_mor_diagram (a : hom(C:=bicat_of_cats) C D') (v : Mon_endo') : Strong_Functor_Category_mor_diagram Mon_endo' domain_action target_action (ab_strong_functor_from_signature sig1) (ab_strong_functor_from_signature sig2) ab_strength_mor_from_signature_mor_nat_trans a v.
proof: Proof. red. cbn. assert (Hyp := pr2 f a v). red in Hyp. cbn in Hyp. etrans. { exact Hyp. } clear Hyp. apply maponpaths_2. apply (horcomp_post_pre _ _ D). Qed.
imports: UniMath.Foundations.PartD UniMath.MoreFoundations.All UniMath.CategoryTheory.Core.Categories UniMath.CategoryTheory.Core.NaturalTransformations UniMath.CategoryTheory.Core.Functors UniMath.CategoryTheory.Core.Isos UniMath.CategoryTheory.FunctorCategory UniMath.CategoryTheory.PointedFunctors UniMath.CategoryTheory.HorizontalComposition UniMath.CategoryTheory.whiskering UniMath.CategoryTheory.PrecategoryBinProduct UniMath.CategoryTheory.Monoidal.AlternativeDefinitions.MonoidalCategoriesTensored UniMath.CategoryTheory.Monoidal.AlternativeDefinitions.MonoidalFunctorsTensored UniMath.CategoryTheory.Adjunctions.Core UniMath.CategoryTheory.Equivalences.Core UniMath.Bicategories.MonoidalCategories.PointedFunctorsMonoidal UniMath.Bicategories.MonoidalCategories.Actions UniMath.Bicategories.MonoidalCategories.ConstructionOfActions UniMath.Bicategories.MonoidalCategories.ActionOfEndomorphismsInBicat UniMath.Bicategories.MonoidalCategories.ActionBasedStrength UniMath.Bicategories.MonoidalCategories.MonoidalFromBicategory UniMath.Bicategories.MonoidalCategories.ActionBasedStrongFunctorCategory UniMath.Bicategories.Core.Bicat UniMath.Bicategories.Core.Examples.BicatOfCats UniMath.SubstitutionSystems.Signatures UniMath.SubstitutionSystems.SignatureCategory UniMath.CategoryTheory.Core.Univalence