Definition op2_left_adjoint_weq_right_adjoint {B : bicat} {x y : B} (f : x --> y) : @left_adjoint (op2_bicat B) _ _ f ≃ @internal_right_adj B _ _ f. Proof. use make_weq. - exact op2_left_adjoint_to_right_adjoint. - use isweq_iso. + exact right_adjoint_to_op2_left_adjoint. + abstract (intro Hf ; use subtypePath ; [ intro ; apply isapropdirprod ; apply cellset_property | ] ; apply idpath). + abstract (intro Hf ; use subtypePath ; [ intro ; apply isapropdirprod ; apply cellset_property | ] ; apply idpath). 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.