proposition: Lemma rad_is_functor : is_functor rad_functor_data.
proof: 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.
imports: UniMath.Foundations.PartD UniMath.Foundations.Propositions UniMath.Foundations.Sets UniMath.MoreFoundations.Tactics UniMath.CategoryTheory.Core.Categories UniMath.CategoryTheory.Core.Functors UniMath.CategoryTheory.Core.Isos UniMath.CategoryTheory.Core.NaturalTransformations UniMath.CategoryTheory.Core.Univalence UniMath.CategoryTheory.FunctorCategory UniMath.CategoryTheory.whiskering UniMath.CategoryTheory.Adjunctions.Core