Definition isEpi_precomp {x y z : C} (f : x --> y) (g : y --> z) : isEpi (f · g) -> isEpi g. Proof. intros X. intros w φ ψ H. apply (maponpaths (λ g', f · g')) in H. repeat rewrite assoc in H. apply (X w _ _ H). Defined.
Require Import UniMath.Foundations.PartD. Require Import UniMath.Foundations.Propositions. Require Import UniMath.Foundations.Sets. Require Import UniMath.CategoryTheory.Core.Categories. Require Import UniMath.CategoryTheory.Core.Isos. Require Import UniMath.CategoryTheory.Core.NaturalTransformations. Require Import UniMath.CategoryTheory.FunctorCategory. Require Import UniMath.CategoryTheory.Subcategory.Core. Require Import UniMath.CategoryTheory.Core.Functors.