proposition: Lemma yoneda_to_presheaf_representable_component_mod_is_nat_trans (f : X --> Y) (Z : B) : is_nat_trans (representable1 B_is_univalent_2_1 f Z : _ ⟶ _) (presheaf_to_yoneda_ob B_is_univalent_2_1 (representable B_is_univalent_2_1 Y) X f Z : _ ⟶ _) (yoneda_to_presheaf_representable_component_mod_component_nat f Z).
proof: Proof. intros h₁ h₂ α. cbn in *. unfold yoneda_to_presheaf_representable_component_mod_component_nat. rewrite id2_left,id2_right. apply idpath. Qed.
imports: UniMath.Foundations.All UniMath.MoreFoundations.All UniMath.CategoryTheory.Core.Categories UniMath.CategoryTheory.Core.Univalence UniMath.CategoryTheory.Core.Isos UniMath.CategoryTheory.Core.Functors UniMath.CategoryTheory.Core.NaturalTransformations UniMath.Bicategories.Core.Bicat UniMath.Bicategories.Core.BicategoryLaws UniMath.Bicategories.Core.Examples.OpMorBicat UniMath.Bicategories.Core.Examples.BicatOfUnivCats UniMath.Bicategories.Core.EquivToAdjequiv UniMath.Bicategories.Core.Unitors UniMath.Bicategories.Morphisms.Adjunctions UniMath.Bicategories.Morphisms.Properties UniMath.Bicategories.Core.Invertible_2cells UniMath.Bicategories.Core.Univalence UniMath.Bicategories.Core.UnivalenceOp UniMath.Bicategories.PseudoFunctors.Display.PseudoFunctorBicat UniMath.Bicategories.PseudoFunctors.PseudoFunctor UniMath.Bicategories.PseudoFunctors.Properties UniMath.Bicategories.Transformations.PseudoTransformation UniMath.Bicategories.Modifications.Modification UniMath.Bicategories.PseudoFunctors.Yoneda UniMath.Bicategories.PseudoFunctors.Representable UniMath.Bicategories.Core.Examples.Image UniMath.Bicategories.PseudoFunctors.Examples.CorestrictImage