Lemma is_functor_yoneda_functor_data (C : category) (c : C) : is_functor (yoneda_ob_functor_data C c). Proof. repeat split; unf; simpl. unfold functor_idax . intros. apply funextsec. intro f. unf. apply id_left. intros a b d f g. 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.