Definition to_universal_equifier_cat_data (cone : equifier_cone) (x : B) : functor_data (hom x cone) (universal_equifier_cat x). Proof. use make_functor_data. - refine (λ h, h · equifier_cone_pr1 cone ,, _) ; cbn. abstract (use (vcomp_lcancel (lassociator _ _ _)) ; [ is_iso | ] ; rewrite <- !lwhisker_lwhisker ; apply maponpaths_2 ; apply maponpaths ; exact (equifier_cone_eq cone)). - exact (λ h₁ h₂ ζ, ζ ▹ _ ,, tt). 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.CategoryTheory.Equivalences.FullyFaithful. Require Import UniMath.CategoryTheory.Subcategory.Core. Require Import UniMath.CategoryTheory.Subcategory.Full. 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.AdjointUnique. Require Import UniMath.Bicategories.Core.Examples.BicatOfUnivCats. Require Import UniMath.Bicategories.Morphisms.Adjunctions. Require Import UniMath.Bicategories.Morphisms.FullyFaithful.