Definition is_invertible_2cell_to_is_nat_z_iso {C D : bicat_of_cats} {F G : C --> D} (η : F ==> G) : is_invertible_2cell η → is_nat_z_iso (pr1 η). Proof. intros Hη X. use tpair. - apply (Hη^-1). - abstract (split ; cbn ; [ exact (nat_trans_eq_pointwise (vcomp_rinv Hη) X) | exact (nat_trans_eq_pointwise (vcomp_linv Hη) X)]). Defined.
Require Import UniMath.Foundations.All. Require Import UniMath.MoreFoundations.All. Require Import UniMath.CategoryTheory.Core.Categories. Require Import UniMath.CategoryTheory.Core.NaturalTransformations. Require Import UniMath.CategoryTheory.Core.Functors. Require Import UniMath.CategoryTheory.whiskering. Require Import UniMath.CategoryTheory.Core.Isos. Require Import UniMath.CategoryTheory.FunctorCategory. Require Import UniMath.CategoryTheory.HorizontalComposition. Require Import UniMath.CategoryTheory.PrecategoryBinProduct. Require Import UniMath.Bicategories.Core.Bicat. Import Bicat.Notations.