Definition bifinal_repr_2cell {X : B} (HX : is_bifinal_repr X) {Y : B} : bifinal_2cell_property X Y. Proof. intros f g. pose (L := functor_to_unit (hom Y X)). pose (R := right_adjoint (HX Y)). pose (η := unit_nat_z_iso_from_adj_equivalence_of_cats (HX Y)). pose (θ₁ := z_iso_to_inv2cell (nat_z_iso_pointwise_z_iso η f)). pose (θ₂ := z_iso_to_inv2cell (nat_z_iso_pointwise_z_iso η g)). exact (comp_of_invertible_2cell θ₁ (inv_of_invertible_2cell θ₂)). 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.Categories.StandardCategories. Require Import UniMath.CategoryTheory.Adjunctions.Core. Require Import UniMath.CategoryTheory.Equivalences.Core. Require Import UniMath.CategoryTheory.Equivalences.CompositesAndInverses. Require Import UniMath.CategoryTheory.Equivalences.FullyFaithful. Require Import UniMath.Bicategories.Core.Bicat. Import Bicat.Notations. Require Import UniMath.Bicategories.Core.Invertible_2cells. Require Import UniMath.Bicategories.Core.Examples.BicatOfUnivCats. Require Import UniMath.Bicategories.Morphisms.Adjunctions. Require Import UniMath.Bicategories.Morphisms.FullyFaithful. Require Import UniMath.Bicategories.Morphisms.Properties.ContainsAdjEquiv. Require Import UniMath.Bicategories.Core.AdjointUnique. Require Import UniMath.Bicategories.Core.EquivToAdjequiv. Require Import UniMath.Bicategories.Core.Univalence.