Definition identity_is_EqualizerIn {y z : C} {f g : y --> z} (E : Equalizer f g) : ∑ φ : C⟦E, E⟧, φ · (EqualizerArrow E) = (EqualizerArrow E). Proof. exists (identity E). apply id_left. 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.