proposition: Lemma presheaf_to_yoneda_ob_pstrans_is_functor (Y : op1_bicat B) : is_functor (presheaf_to_yoneda_ob_pstrans_functor_data Y).
proof: Proof. split. - intro f ; cbn. unfold presheaf_to_yoneda_ob_pstrans_functor_mor ; unfold presheaf_to_yoneda_ob_pstrans_functor_ob. exact (nat_trans_eq_pointwise (psfunctor_id2 F f) x). - intros f₁ f₂ f₃ α₁ α₂ ; cbn. unfold presheaf_to_yoneda_ob_pstrans_functor_mor. exact (nat_trans_eq_pointwise (psfunctor_vcomp F α₁ α₂) x). 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