Lemma comp_faithful_is_faithful (C D E : precategory) (F : functor C D) (faithF : faithful F) (G : functor D E) (faithG : faithful G) : faithful (functor_composite F G). Proof. unfold faithful in *. intros ? ?; apply (isinclcomp (_,, faithF _ _) (_,, faithG _ _)). Qed.
Require Import UniMath.Foundations.PartD. Require Import UniMath.Foundations.Propositions. Require Import UniMath.Foundations.Sets. Require Import UniMath.MoreFoundations.PartA. Require Import UniMath.MoreFoundations.Univalence. Require Import UniMath.MoreFoundations.Tactics. Require Import UniMath.CategoryTheory.Core.Categories. Require Import UniMath.CategoryTheory.Core.Isos. Require Import UniMath.CategoryTheory.Core.TransportMorphisms. Require Import UniMath.CategoryTheory.Core.Univalence.