Lemma isweq_idtoiso_functorcat (C : precategory_data) (D : category) (H : is_univalent D) (F G : ob [C, D, D]) : isweq (@idtoiso _ F G). Proof. apply (isweq_iso _ (functor_eq_from_functor_z_iso H F G)). apply functor_eq_from_functor_z_iso_idtoiso. apply idtoiso_functor_eq_from_functor_z_iso. Defined.
Require Import UniMath.Foundations.Propositions. Require Import UniMath.MoreFoundations.Tactics. Require Import UniMath.MoreFoundations.Univalence. Require Import UniMath.CategoryTheory.Core.Categories. Require Import UniMath.CategoryTheory.Core.Isos. Require Import UniMath.CategoryTheory.Core.TransportMorphisms. Require Import UniMath.CategoryTheory.Core.Functors. Require Import UniMath.CategoryTheory.Core.NaturalTransformations. Require Import UniMath.CategoryTheory.Core.Univalence.