proposition: Lemma yy_natural (F : PreShv C) (c : C) (A : (F : C^op ⟶ SET) c : hSet) c' (f : C⟦c', c⟧) : yy (functor_on_morphisms (F : C^op ⟶ SET) f A) = functor_on_morphisms (yoneda C) f · yy A.
proof: Proof. assert (XTT := is_natural_yoneda_iso_inv _ F _ _ f). apply (toforallpaths _ _ _ XTT). Qed.
imports: UniMath.Foundations.All UniMath.MoreFoundations.All UniMath.CategoryTheory.Core.Prelude UniMath.CategoryTheory.Core.Isos UniMath.CategoryTheory.Core.NaturalTransformations UniMath.CategoryTheory.Core.Univalence UniMath.CategoryTheory.opp_precat UniMath.CategoryTheory.Core.Functors UniMath.CategoryTheory.PrecategoryBinProduct UniMath.CategoryTheory.Categories.HSET.All UniMath.CategoryTheory.whiskering UniMath.CategoryTheory.yoneda UniMath.CategoryTheory.Limits.Pullbacks UniMath.CategoryTheory.DisplayedCats.Core UniMath.CategoryTheory.DisplayedCats.Constructions UniMath.Bicategories.Core.Bicat UniMath.Bicategories.Morphisms.Adjunctions UniMath.Bicategories.Core.Invertible_2cells UniMath.Bicategories.Core.Univalence UniMath.Bicategories.DisplayedBicats.Examples.ContravariantFunctor UniMath.Bicategories.Core.Examples.BicatOfUnivCats UniMath.Bicategories.DisplayedBicats.Examples.Cofunctormap UniMath.Bicategories.DisplayedBicats.Examples.FullSub UniMath.Bicategories.DisplayedBicats.Examples.Sigma UniMath.Bicategories.DisplayedBicats.DispBicat UniMath.Bicategories.DisplayedBicats.DispAdjunctions UniMath.Bicategories.DisplayedBicats.DispUnivalence UniMath.Bicategories.DisplayedBicats.DispInvertibles UniMath.Bicategories.DisplayedBicats.Examples.Prod UniMath.Bicategories.DisplayedBicats.Examples.DisplayedCatToBicat