Lemma covyoneda_iso_sets (C : category) (c : C) (F : functor C HSET) : is_z_isomorphism (C:=HSET) (a := make_hSet _ (isaset_nat_trans_covyoneda C c F)) (covyoneda_map_1 C c F). Proof. set (T:= covyoneda_map_2 C c F). exists T. split; simpl. - apply funextsec; intro alpha. unf; simpl. apply (covyoneda_map_1_2 C c F). - apply funextsec; intro x. unf; rewrite (functor_id F). apply idpath. Defined.
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.