Definition isMonic_postcomp {x y z : C} (f : x --> y) (g : y --> z) : isMonic (f · g) -> isMonic f. Proof. intros X. intros w φ ψ H. apply (maponpaths (λ f', f' · g)) in H. repeat rewrite <- assoc in H. apply (X w _ _ H). Defined.
Require Import UniMath.Foundations.All. Require Import UniMath.MoreFoundations.All. Require Import UniMath.CategoryTheory.Categories.HSET.Core. Require Import UniMath.CategoryTheory.Core.Categories. Require Import UniMath.CategoryTheory.Core.Functors. Require Import UniMath.CategoryTheory.Core.Isos. Require Import UniMath.CategoryTheory.Core.NaturalTransformations. Require Import UniMath.CategoryTheory.Core.Univalence. Require Import UniMath.CategoryTheory.covyoneda. Require Import UniMath.CategoryTheory.FunctorCategory. Require Import UniMath.CategoryTheory.Subcategory.Core.