Lemma isiso_from_Equalizer_to_Equalizer {y z : C} {f g : y --> z} (E E' : Equalizer f g) : is_iso (from_Equalizer_to_Equalizer E E'). Proof. apply (is_iso_qinv _ (from_Equalizer_to_Equalizer E' E)). apply are_inverses_from_Equalizer_to_Equalizer. 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.