Definition invertible_2cell_is_nat_z_iso {C D : bicat_of_cats} (F G : C --> D) : nat_z_iso F G ≃ invertible_2cell F G. Proof. use make_weq. - exact (nat_z_iso_to_invertible_2cell F G). - use isweq_iso. + exact (invertible_2cell_to_nat_z_iso F G). + intros x. use subtypePath. * intro. apply isaprop_is_nat_z_iso. * apply idpath. + intros x. use subtypePath. * intro. apply isaprop_is_invertible_2cell. * apply idpath. 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.