proposition: Lemma is_functor_yoneda_functor_data (C : category) (c : C) : is_functor (yoneda_ob_functor_data C c).
proof: 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.
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