Definition biadj_hom_right_left_data : nat_trans_data (biadj_right_hom ∙ biadj_left_hom) (functor_identity (hom (L X) Y)). Proof. intros f. exact (((psfunctor_comp L (η X) (#R f))^-1 ▹ (ε Y)) • rassociator _ _ _ • (#L (η X) ◃ (psnaturality_of ε f)^-1) • lassociator _ _ _ • (((_ ◃ (rinvunitor _ • linvunitor _)) • linvunitor _ • (invertible_modcomponent_of (biadj_triangle_l R) X)) ▹ f) • lunitor f). Defined.
Require Import UniMath.Foundations.All. Require Import UniMath.MoreFoundations.All. Require Import UniMath.CategoryTheory.Core.Categories. Require Import UniMath.CategoryTheory.Core.Isos. Require Import UniMath.CategoryTheory.Core.Functors. Require Import UniMath.CategoryTheory.Core.NaturalTransformations. 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.Univalence. Require Import UniMath.Bicategories.Core.BicategoryLaws. Require Import UniMath.Bicategories.PseudoFunctors.Display.PseudoFunctorBicat. Require Import UniMath.Bicategories.PseudoFunctors.PseudoFunctor. Import PseudoFunctor.Notations. Require Import UniMath.Bicategories.PseudoFunctors.Examples.Identity. Require Import UniMath.Bicategories.PseudoFunctors.Examples.Composition. Require Import UniMath.Bicategories.Transformations.PseudoTransformation. Require Import UniMath.Bicategories.Transformations.Examples.Whiskering. Require Import UniMath.Bicategories.Transformations.Examples.Unitality. Require Import UniMath.Bicategories.Transformations.Examples.Associativity. Require Import UniMath.Bicategories.Modifications.Modification.