Lemma functor_preserves_split_epi {C D : precategory} (F : functor C D) {A B : ob C} (f : C⟦A,B⟧) : is_split_epi f -> is_split_epi (# F f). Proof. intro hf. exists (#F (pr1 hf)). unfold is_retraction. now rewrite <- functor_id, <- (pr2 hf), <- functor_comp. 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.