Definition right_biadj_preserves_equifiers_commute (x : B₁) : biadj_left_hom R x e ∙ to_universal_equifier_cat e (L x) ∙ full_sub_category_functor (λ (h : hom (L x) y₁), make_hProp (h ◃ α = h ◃ β) (cellset_property _ _ _ _)) (λ (h : hom x (R y₁)), make_hProp (h ◃ ## R α = h ◃ ## R β) (cellset_property _ _ _ _)) (biadj_right_hom R x y₁) preserve_equifiers_R_path ⟹ to_universal_equifier_cat (psfunctor_equifier_cone R e) x. Proof. use make_nat_trans. - exact (right_biadj_preserves_equifiers_commute_data x). - exact (right_biadj_preserves_equifiers_commute_is_nat_trans x). 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.Univalence. Require Import UniMath.CategoryTheory.Core.Functors. Require Import UniMath.CategoryTheory.Core.NaturalTransformations. Require Import UniMath.CategoryTheory.Categories.StandardCategories. Require Import UniMath.CategoryTheory.Subcategory.Full. Require Import UniMath.CategoryTheory.Subcategory.FullEquivalences. Require Import UniMath.CategoryTheory.Adjunctions.Core. Require Import UniMath.CategoryTheory.Equivalences.Core. Require Import UniMath.CategoryTheory.Equivalences.CompositesAndInverses. Require Import UniMath.Bicategories.Core.Bicat. Import Bicat.Notations. Require Import UniMath.Bicategories.Core.Invertible_2cells. Require Import UniMath.Bicategories.Core.EquivToAdjequiv. Require Import UniMath.Bicategories.Core.Examples.BicatOfUnivCats. Require Import UniMath.Bicategories.Morphisms.Adjunctions. Require Import UniMath.Bicategories.Morphisms.Properties. Require Import UniMath.Bicategories.Morphisms.Properties.ClosedUnderInvertibles. 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.PseudoFunctors.Biadjunction. Require Import UniMath.Bicategories.PseudoFunctors.Preservation.Preservation. Require Import UniMath.Bicategories.Transformations.PseudoTransformation. Require Import UniMath.Bicategories.Modifications.Modification. Require Import UniMath.Bicategories.Limits.Equifiers.