Definition op2_left_adjoint_right_adjoint_is_left_adjoint {B : bicat} {x y : B} {f : x --> y} (Hf : @left_adjoint (op2_bicat B) _ _ f) : @left_adjoint B _ _ (left_adjoint_right_adjoint Hf). Proof. simple refine ((_ ,, (_ ,, _)) ,, (_ ,, _)). - exact f. - exact (left_adjoint_counit Hf). - exact (left_adjoint_unit Hf). - abstract (cbn ; rewrite !vassocl ; exact (internal_triangle2 Hf)). - abstract (cbn ; rewrite !vassocl ; exact (internal_triangle1 Hf)). 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.Invertible_2cells. Require Import UniMath.Bicategories.Core.Unitors. Require Import UniMath.Bicategories.Core.BicategoryLaws. Require Import UniMath.Bicategories.Core.EquivToAdjequiv. Require Import UniMath.Bicategories.Core.Examples.OpCellBicat. Require Import UniMath.Bicategories.Morphisms.Adjunctions. Require Import UniMath.Bicategories.Morphisms.FullyFaithful. Require Import UniMath.Bicategories.Morphisms.DiscreteMorphisms.