Lemma merely_split_monic_is_monic (m : A --> B) : has_homsets C -> is_merely_split_monic m -> isMonic m. Proof. intros H. apply merely_split_monic_to_split_monic. - apply isapropisMonic; auto. - apply split_monic_is_monic. 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.