Definition is_invertible_equifier_ump_cell {x : B} {u₁ u₂ : x --> cone} (ζ : u₁ · equifier_cone_pr1 cone ==> u₂ · equifier_cone_pr1 cone) (Hζ : is_invertible_2cell ζ) : is_invertible_2cell (equifier_ump_cell ζ). Proof. use make_is_invertible_2cell. - exact (equifier_ump_cell (Hζ^-1)). - abstract (use (equifier_ump_eq_alt (id2 _)) ; rewrite <- !rwhisker_vcomp ; rewrite !equifier_ump_cell_pr1 ; rewrite vcomp_rinv ; rewrite id2_rwhisker ; apply idpath). - abstract (use (equifier_ump_eq_alt (id2 _)) ; rewrite <- !rwhisker_vcomp ; rewrite !equifier_ump_cell_pr1 ; rewrite vcomp_linv ; rewrite id2_rwhisker ; 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.Core.NaturalTransformations. Require Import UniMath.CategoryTheory.Core.Isos. Require Import UniMath.CategoryTheory.Core.Univalence. Require Import UniMath.CategoryTheory.Adjunctions.Core. Require Import UniMath.CategoryTheory.Equivalences.Core. Require Import UniMath.CategoryTheory.Equivalences.FullyFaithful. Require Import UniMath.CategoryTheory.Subcategory.Core. Require Import UniMath.CategoryTheory.Subcategory.Full. Require Import UniMath.Bicategories.Core.Bicat. Import Bicat.Notations. Require Import UniMath.Bicategories.Core.Invertible_2cells. Require Import UniMath.Bicategories.Core.Univalence. Require Import UniMath.Bicategories.Core.AdjointUnique. Require Import UniMath.Bicategories.Core.Examples.BicatOfUnivCats. Require Import UniMath.Bicategories.Morphisms.Adjunctions. Require Import UniMath.Bicategories.Morphisms.FullyFaithful.