proposition: Lemma yy_comp_nat_trans (F F' : PreShv C) (p : _ ⟦F, F'⟧) A (v : (F : C^op ⟶ SET) A : hSet) : yy v · p = yy ((p : nat_trans _ _ ) _ v).
proof: Proof. apply nat_trans_eq. - apply has_homsets_HSET. - intro c. simpl. apply funextsec. intro f. cbn. assert (XR := toforallpaths _ _ _ (nat_trans_ax p _ _ f) v ). cbn in XR. apply XR. 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