proposition: Lemma essentially_surjective_2_from_comp {C C' C'' : category} (F : C ⟶ C') (F' : C' ⟶ C'') (H : essentially_surjective (functor_composite F F')) : essentially_surjective F'.
proof: Proof. intro. refine (hinhfun _ (H b)). intro x. exists (F (pr1 x)). exact (pr2 x). Qed.
imports: UniMath.Foundations.PartD UniMath.Foundations.Propositions UniMath.Foundations.Sets UniMath.MoreFoundations.PartA UniMath.MoreFoundations.Univalence UniMath.MoreFoundations.Tactics UniMath.CategoryTheory.Core.Categories UniMath.CategoryTheory.Core.Isos UniMath.CategoryTheory.Core.TransportMorphisms UniMath.CategoryTheory.Core.Univalence