Proposition regular_epi_mono_factorization_comm : f = e · m. Proof. unfold e, m. unfold regular_epi_mono_factorization_epi, regular_epi_mono_factorization_mono. rewrite CoequalizerCommutes. apply idpath. Qed.
Require Import UniMath.Foundations.All. Require Import UniMath.MoreFoundations.All. Require Import UniMath.CategoryTheory.Core.Prelude. Require Import UniMath.CategoryTheory.Limits.Terminal. Require Import UniMath.CategoryTheory.Limits.Pullbacks. Require Import UniMath.CategoryTheory.Limits.Coequalizers. Require Import UniMath.CategoryTheory.Monics. Require Import UniMath.CategoryTheory.Epis. Require Import UniMath.CategoryTheory.EpiFacts. Require Import UniMath.CategoryTheory.RegularAndExact.RegularEpi.