Definition equalizer_of_setcategory_precategory_ob_mor {C₁ C₂ : setcategory} (F G : C₁ ⟶ C₂) : precategory_ob_mor. Proof. use make_precategory_ob_mor. - exact (∑ (x : C₁), F x = G x). - exact (λ x y, ∑ (f : pr1 x --> pr1 y), # F f · idtoiso (pr2 y) = idtoiso (pr2 x) · # G f). 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.