Lemma rad_eps_is_nat_trans : is_nat_trans (functor_composite rad F) (functor_identity B) (λ b, rad_eps b). Proof. unfold is_nat_trans. simpl. intros b b' g. unfold rad_mor; unfold fully_faithful_inv_hom. set (H3 := homotweqinvweq (weq_from_fully_faithful HF (pr1 rad b) (pr1 rad b'))). simpl in *. rewrite H3; clear H3. repeat rewrite <- assoc. rewrite z_iso_after_z_iso_inv, id_right. apply idpath. Qed.
Require Import UniMath.Foundations.PartD. Require Import UniMath.Foundations.Propositions. Require Import UniMath.Foundations.Sets. Require Import UniMath.MoreFoundations.Tactics. 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.Core.Univalence. Require Import UniMath.CategoryTheory.FunctorCategory. Require Import UniMath.CategoryTheory.whiskering. Require Import UniMath.CategoryTheory.Adjunctions.Core.