Lemma functor_on_iso_is_iso (C C' : precategory) (F : functor C C') (a b : ob C) (f : iso a b) : is_iso (#F f). Proof. apply (is_iso_qinv _ (#F (inv_from_iso f))). apply is_inverse_functor_image. Defined.
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.