Definition bicat_invertible_2cell_is_op1_bicat_invertible_2cell {C : bicat} {X Y : op1_bicat C} (f g : X --> Y) : @invertible_2cell C Y X f g ≃ invertible_2cell f g. Proof. use weqfibtototal. intro α. apply op1_bicat_is_invertible_2cell_is_bicat_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.