Definition make_biadj_data {B₁ B₂ : bicat} {L : psfunctor B₁ B₂} (R : left_biadj_unit_counit L) (tl : biadj_triangle_l_law R) (tr : biadj_triangle_r_law R) : left_biadj_data L := R ,, tl ,, tr. Section BiadjunctionHom. Context {B₁ B₂ : bicat} {L : psfunctor B₁ B₂} (R : left_biadj_data L) (X : B₁) (Y : B₂). Let η : pstrans (id_psfunctor B₁) (comp_psfunctor R L) := biadj_unit R. Let ε : pstrans (comp_psfunctor L R) (id_psfunctor B₂) := biadj_counit R. Local Definition biadj_left_hom_data : functor_data (hom X (R Y)) (hom (L X) Y). Proof. use make_functor_data. - exact (λ f, #L f · ε Y). - exact (λ f g α, (##L α) ▹ ε Y). 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.