Lemma rad_is_functor : is_functor rad_functor_data. Proof. split. simpl. intro b. simpl. unfold rad_mor. simpl. rewrite id_right, z_iso_inv_after_z_iso, fully_faithful_inv_identity. apply idpath. intros a b c f g. simpl. unfold rad_mor; simpl. rewrite <- fully_faithful_inv_comp. apply maponpaths. repeat rewrite <- assoc. repeat apply maponpaths. rewrite assoc. rewrite z_iso_after_z_iso_inv, id_left. 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.