Definition grpds_2cell_to_nat_z_iso {G₁ G₂ : grpds} {F₁ F₂ : G₁ --> G₂} (α : F₁ ==> F₂) : nat_z_iso (pr1 F₁) (pr1 F₂). Proof. use make_nat_z_iso. - exact (pr1 α). - intros x. exact (pr2 G₂ (pr11 F₁ x) (pr11 F₂ x) (pr11 α x)). Defined.
Require Import UniMath.Foundations.All. Require Import UniMath.MoreFoundations.All. Require Import UniMath.CategoryTheory.Core.Categories. Require Import UniMath.CategoryTheory.Core.Isos. Require Import UniMath.CategoryTheory.Core.Functors. Require Import UniMath.CategoryTheory.Core.NaturalTransformations. Require Import UniMath.CategoryTheory.Core.Univalence. Require Import UniMath.CategoryTheory.Groupoids. Require Import UniMath.Bicategories.Core.Bicat. Import Bicat.Notations. Require Import UniMath.Bicategories.Morphisms.Adjunctions. Require Import UniMath.Bicategories.Core.EquivToAdjequiv. Require Import UniMath.Bicategories.Core.AdjointUnique. Require Import UniMath.Bicategories.Core.Univalence. Require Import UniMath.Bicategories.Core.Examples.BicatOfUnivCats. Require Import UniMath.Bicategories.DisplayedBicats.Examples.FullSub.