Definition equalizer_of_setcategory_pr1 {C₁ C₂ : setcategory} (F G : C₁ ⟶ C₂) : equalizer_of_setcategory F G ⟶ C₁. Proof. use make_functor. - use make_functor_data. + exact (λ x, pr1 x). + exact (λ x y f, pr1 f). - abstract (split ; intro ; intros ; apply idpath). Defined.
Require Import UniMath.Foundations.All. Require Import UniMath.MoreFoundations.All. Require Import UniMath.CategoryTheory.Core.Categories. Require Import UniMath.CategoryTheory.Core.Univalence. Require Import UniMath.CategoryTheory.Core.Isos. Require Import UniMath.CategoryTheory.Core.Setcategories. Require Import UniMath.CategoryTheory.Core.Functors. Require Import UniMath.CategoryTheory.Core.NaturalTransformations. Require Import UniMath.CategoryTheory.Categories.CategoryOfSetCategories. Require Import UniMath.CategoryTheory.Limits.Equalizers.