Definition left_adjoint_to_adjunction_cat (w : B) (HB_2_1 : is_univalent_2_1 B) : @adjunction bicat_of_univ_cats (univ_hom HB_2_1 w x) (univ_hom HB_2_1 w y). Proof. refine (post_comp w l ,, ((post_comp w r ,, (left_adjoint_to_repr_unit w ,, left_adjoint_to_repr_counit w)) ,, (_ ,, _))). - abstract (use nat_trans_eq ; [ apply homset_property | ] ; cbn ; intro ; rewrite !id2_right, id2_left ; apply left_adjoint_to_left_adjoint_repr_form_adjunction). - abstract (use nat_trans_eq ; [ apply homset_property | ] ; cbn ; intro ; rewrite !id2_right, id2_left ; apply left_adjoint_to_left_adjoint_repr_form_adjunction). 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.Core.NaturalTransformations. Require Import UniMath.CategoryTheory.Core.Isos. Require Import UniMath.CategoryTheory.Core.Univalence. Require Import UniMath.CategoryTheory.Adjunctions.Core. Require Import UniMath.CategoryTheory.Equivalences.Core. Require Import UniMath.Bicategories.Core.Bicat. Import Bicat.Notations. Require Import UniMath.Bicategories.Core.Invertible_2cells. Require Import UniMath.Bicategories.Core.BicategoryLaws. Require Import UniMath.Bicategories.Core.Unitors. Require Import UniMath.Bicategories.Core.EquivToAdjequiv. Require Import UniMath.Bicategories.Core.Univalence. Require Import UniMath.Bicategories.Core.AdjointUnique. Require Import UniMath.Bicategories.Core.Examples.BicatOfUnivCats. Require Import UniMath.Bicategories.Morphisms.Adjunctions.