Lemma merely_split_epi_is_epi (f : A --> B) : has_homsets C -> is_merely_split_epi f -> isEpi f. Proof. intros H. apply merely_split_epi_to_split_epi. - apply isapropisEpi; auto. - apply split_epi_is_epi. 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.