Lemma functor_iso_if_pointwise_iso (C : precategory_data) (C' : precategory) (hs: has_homsets C') (F G : ob [C, C', hs]) (A : F --> G) : is_nat_iso A -> is_iso A . Proof. intro H. apply (is_iso_qinv _ (nat_trans_inv_from_pointwise_inv _ _ _ _ _ _ H)). simpl; apply is_inverse_nat_trans_inv_from_pointwise_inv. 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.