proposition: Lemma is_functor_covyoneda (C : category) : is_functor (covyoneda_functor_data C).
proof: Proof. split. - intro a. apply (@nat_trans_eq C _ has_homsets_HSET). intro c; apply funextsec; intro f; simpl in *. apply id_left. - intros a b c f g. apply (@nat_trans_eq C _ has_homsets_HSET). simpl; intro d; apply funextsec; intro h; apply pathsinv0, assoc. Qed.
imports: UniMath.Foundations.PartD UniMath.Foundations.Propositions UniMath.Foundations.Sets UniMath.CategoryTheory.Core.Functors UniMath.CategoryTheory.Core.Categories UniMath.CategoryTheory.Core.NaturalTransformations UniMath.CategoryTheory.FunctorCategory UniMath.CategoryTheory.opp_precat UniMath.CategoryTheory.Categories.HSET.Core UniMath.CategoryTheory.Core.Functors UniMath.CategoryTheory.whiskering