Lemma is_nat_trans_yoneda_morphisms_data (C : category) (c c' : ob C) (f : hom C c c') : is_nat_trans (yoneda_objects C c) (yoneda_objects C c') (yoneda_morphisms_data C c c' f). Proof. unfold is_nat_trans; simpl. unfold yoneda_morphisms_data; simpl. intros d d' g. apply funextsec; simpl in *. unfold yoneda_objects_ob; simpl. unf; intro; apply ( ! assoc _ _ _ ). Qed.
Require Import UniMath.Foundations.PartD. Require Import UniMath.Foundations.Propositions. Require Import UniMath.Foundations.Sets. Require Import UniMath.CategoryTheory.Core.Categories. Require Import UniMath.CategoryTheory.Core.Functors. Require Import UniMath.CategoryTheory.Core.Isos. Require Import UniMath.CategoryTheory.Core.NaturalTransformations. Require Import UniMath.CategoryTheory.opp_precat. Require Import UniMath.CategoryTheory.Categories.HSET.Core. Require Import UniMath.CategoryTheory.Categories.HSET.MonoEpiIso. Require Import UniMath.CategoryTheory.whiskering.