Lemma comp_full_is_full (C D E : precategory) (F : functor C D) (fullF : full F) (G : functor D E) (fullG : full G) : full (functor_composite F G). Proof. unfold full in *. intros ? ?; apply (issurjcomp _ _ (fullF _ _) (fullG _ _)). 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.