Definition op1_bicat_is_invertible_2cell_is_bicat_is_invertible_2cell {C : bicat} {X Y : op1_bicat C} {f g : X --> Y} (α : f ==> g) : @is_invertible_2cell C Y X f g α ≃ is_invertible_2cell α. Proof. use weqimplimpl. - exact (bicat_is_invertible_2cell_to_op1_bicat_is_invertible_2cell α). - exact (op1_bicat_is_invertible_2cell_to_bicat_is_invertible_2cell α). - apply isaprop_is_invertible_2cell. - apply isaprop_is_invertible_2cell. 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.opp_precat. Require Import UniMath.CategoryTheory.PrecategoryBinProduct. Require Import UniMath.Bicategories.Core.Bicat. Import Bicat.Notations. Require Import UniMath.Bicategories.Core.Invertible_2cells. Require Import UniMath.Bicategories.Morphisms.Adjunctions.