Lemma functor_full_img_essentially_surjective (A B : category) (F : functor A B) : essentially_surjective (functor_full_img F). Proof. intro b. use (pr2 b). intros [c h] q Hq. apply Hq. exists c. apply iso_in_sub_from_iso. apply h. Qed.
Require Import UniMath.Foundations.Sets. Require Import UniMath.MoreFoundations.PartA. Require Import UniMath.CategoryTheory.Core.Categories. Require Import UniMath.CategoryTheory.Core.Isos. Require Import UniMath.CategoryTheory.Core.Univalence. Require Import UniMath.CategoryTheory.Core.Functors. Require Import UniMath.CategoryTheory.Core.NaturalTransformations. Require Import UniMath.CategoryTheory.Subcategory.Core.