Definition equalizer_of_setcategory_precategory_data {C₁ C₂ : setcategory} (F G : C₁ ⟶ C₂) : precategory_data. Proof. use make_precategory_data. - exact (equalizer_of_setcategory_precategory_ob_mor F G). - cbn ; refine (λ x, identity _ ,, _). abstract (rewrite !functor_id ; rewrite id_left, id_right ; apply idpath). - cbn ; refine (λ x y z f g, pr1 f · pr1 g ,, _). abstract (rewrite !functor_comp ; rewrite !assoc ; rewrite <- (pr2 f) ; rewrite !assoc' ; rewrite <- (pr2 g) ; 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.