Lemma is_z_iso_yoneda_functor_precomp : is_z_isomorphism yoneda_functor_precomp. Proof. apply nat_trafo_z_iso_if_pointwise_z_iso. intro a. simpl. set (T:= make_weq _ (Fff a c)). set (TA := make_hSet (hom C a c) (homset_property C _ _)). set (TB := make_hSet (hom D (F a) (F c)) (homset_property _ _ _ )). apply (hset_equiv_is_z_iso TA TB T). 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.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.