proposition: Lemma yoneda_map_2_ax (C : category) (c : C) (F : functor C^op HSET) (x : pr1 (F c)) : is_nat_trans (pr1 (yoneda C c)) F (fun (d : C) (f : hom (C ^op) c d) => #F f x).
proof: Proof. intros a b f; simpl in *. apply funextsec. unfold yoneda_objects_ob; intro g. set (H:= @functor_comp _ _ F _ _ b g). unfold functor_comp in H; unfold opp_precat_data in H; simpl in *. apply (toforallpaths _ _ _ (H f) x). Qed.
imports: UniMath.Foundations.PartD UniMath.Foundations.Propositions UniMath.Foundations.Sets UniMath.CategoryTheory.Core.Categories UniMath.CategoryTheory.Core.Functors UniMath.CategoryTheory.Core.Isos UniMath.CategoryTheory.Core.NaturalTransformations UniMath.CategoryTheory.FunctorCategory UniMath.CategoryTheory.opp_precat UniMath.CategoryTheory.Categories.HSET.Core UniMath.CategoryTheory.Categories.HSET.MonoEpiIso UniMath.CategoryTheory.whiskering