Lemma is_functor_covyoneda (C : category) : is_functor (covyoneda_functor_data C). 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.
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.NaturalTransformations. Require Import UniMath.CategoryTheory.Core.Isos. Require Import UniMath.CategoryTheory.opp_precat. Require Import UniMath.CategoryTheory.Categories.HSET.Core. Require Import UniMath.CategoryTheory.Core.Functors. Require Import UniMath.CategoryTheory.whiskering.