Definition op1_bicat_left_adjoint_equivalence_is_bicat_left_adjoint_equivalence {C : bicat} {X Y : op1_bicat C} (f : X --> Y) : @left_adjoint_equivalence C Y X f ≃ left_adjoint_equivalence f. Proof. use make_weq. - exact (bicat_left_adjoint_equivalence_to_op1_bicat_left_adjoint_equivalence f). - use isweq_iso. + exact (op1_bicat_left_adjoint_equivalence_to_bicat_left_adjoint_equivalence f). + intros x. use subtypePath. * intro. do 2 apply isapropdirprod ; try (apply C) ; apply isaprop_is_invertible_2cell. * apply idpath. + intros x. use subtypePath. * intro. do 2 apply isapropdirprod ; try (apply C) ; 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.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.