Definition inv_equiv {C : bicat} {X Y : C} {f : X --> Y} (Hf : left_equivalence f) : left_equivalence (pr11 Hf). Proof. use tpair. - use tpair. + exact f. + split. * exact ((left_equivalence_counit_iso Hf)^-1). * exact ((left_equivalence_unit_iso Hf)^-1). - split ; cbn ; is_iso. Defined.
Require Import UniMath.Foundations.All. Require Import UniMath.MoreFoundations.All. Require Import UniMath.CategoryTheory.Core.Categories. Require Import UniMath.Bicategories.Core.Bicat. Import Bicat.Notations. Require Import UniMath.Bicategories.Core.Unitors. Require Import UniMath.Bicategories.Core.Invertible_2cells. Require Import UniMath.Bicategories.Core.BicategoryLaws. Require Import UniMath.Bicategories.Morphisms.Adjunctions. Require Import UniMath.Bicategories.Core.Univalence.