Lemma EqualizerCommutes {y z : C} {f g : y --> z} (E : Equalizer f g) (w : C) (h : w --> y) (H : h · f = h · g) : (EqualizerIn E w h H) · (EqualizerArrow E) = h. Proof. exact (pr2 (pr1 ((isEqualizer_Equalizer E) w h H))). Defined.
Require Import UniMath.Foundations.All. Require Import UniMath.MoreFoundations.All. Require Import UniMath.CategoryTheory.Core.Categories. Require Import UniMath.CategoryTheory.Core.Isos. Require Import UniMath.CategoryTheory.Core.Univalence. Require Import UniMath.CategoryTheory.Monics. Require Import UniMath.CategoryTheory.Retracts.