Definition to_op2_left_adjequiv {B : bicat} {x y : op2_bicat B} (f : x --> y) : @left_adjoint_equivalence B x y f → left_adjoint_equivalence f. Proof. intros Hf. simple refine ((_ ,, (_ ,, _)) ,, ((_ ,, _) ,, (_ ,, _))). - exact (left_adjoint_right_adjoint Hf). - exact ((left_equivalence_unit_iso Hf)^-1). - exact ((left_equivalence_counit_iso Hf)^-1). - abstract (use inv_cell_eq ; cbn ; [ apply to_op2_is_invertible_2cell ; is_iso | apply to_op2_is_invertible_2cell ; is_iso | exact (internal_triangle1 Hf) ]). - abstract (use inv_cell_eq ; cbn ; [ apply to_op2_is_invertible_2cell ; is_iso | apply to_op2_is_invertible_2cell ; is_iso | exact (internal_triangle2 Hf)]). - cbn. apply to_op2_is_invertible_2cell. is_iso. - cbn. apply to_op2_is_invertible_2cell. is_iso. 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.