Definition iso_in_E₂_weq {x y : E₂} (f g : x --> y) : invertible_2cell (mor_E₂_to_E₁ f) (mor_E₂_to_E₁ g) ≃ invertible_2cell f g. Proof. use make_weq. - exact (iso_in_E₂ f g). - use isweq_iso. + exact (iso_in_E₂_inv f g). + intros α. use subtypePath. { intro ; apply isaprop_is_invertible_2cell. } apply idpath. + intros α. 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.Functors. Require Import UniMath.CategoryTheory.PrecategoryBinProduct. Require Import UniMath.CategoryTheory.DisplayedCats.Core. Require Import UniMath.CategoryTheory.DisplayedCats.Constructions. Require Import UniMath.Bicategories.Core.Bicat. Import Bicat.Notations. Require Import UniMath.Bicategories.DisplayedBicats.DispBicat. Import DispBicat.Notations. Require Import UniMath.Bicategories.Core.EquivToAdjequiv. Require Import UniMath.Bicategories.Core.AdjointUnique. Require Import UniMath.Bicategories.DisplayedBicats.DispInvertibles. Require Import UniMath.Bicategories.DisplayedBicats.DispAdjunctions. Require Import UniMath.Bicategories.DisplayedBicats.DispUnivalence.