Definition right_adjoint_to_op2_left_adjoint {B : bicat} {x y : B} {f : x --> y} (Hf : @internal_right_adj B _ _ f) : @left_adjoint (op2_bicat B) _ _ f. Proof. simple refine ((_ ,, (_ ,, _)) ,, (_ ,, _)). - exact (internal_right_adj_left_adjoint Hf). - exact (internal_right_adj_counit Hf). - exact (internal_right_adj_unit Hf). - abstract (cbn ; rewrite !vassocr ; exact (pr22 Hf)). - abstract (cbn ; rewrite !vassocr ; exact (pr12 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.