Lemma split_epi_is_epi (f : A --> B) : is_split_epi f -> isEpi f. Proof. intros is_split. apply (isEpi_precomp _ (pr1 is_split) f). apply (transportf _ (!pr2 is_split)). apply identity_isEpi. Qed.
Require Import UniMath.Foundations.PartD. Require Import UniMath.Foundations.Propositions. Require Import UniMath.MoreFoundations.Tactics. Require Import UniMath.CategoryTheory.Core.Categories. Require Import UniMath.CategoryTheory.Core.Isos. Require Import UniMath.CategoryTheory.Core.Functors. Require Import UniMath.CategoryTheory.Monics. Require Import UniMath.CategoryTheory.Epis. Require Import UniMath.CategoryTheory.Retracts.