Lemma is_functor_yoneda (C : category) : is_functor (yoneda_functor_data C). Proof. unfold is_functor. repeat split; simpl. intro a. set (T:= nat_trans_eq (C:=C^op) (has_homsets_HSET)). simpl. apply T. intro c; apply funextsec; intro f. apply id_right. intros a b c f g. set (T:=nat_trans_eq (C:=C^op) (has_homsets_HSET)). apply T. simpl; intro d; apply funextsec; intro h. 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.