Lemma pre_composition_with_ess_surj_and_full_is_fully_faithful : fully_faithful (pre_composition_functor A B C H). Proof. apply full_and_faithful_implies_fully_faithful. apply pre_composition_with_ess_surj_and_full_is_full_and_faithful. Defined.
Require Import UniMath.Foundations.PartD. Require Import UniMath.Foundations.Propositions. Require Import UniMath.Foundations.Sets. Require Import UniMath.CategoryTheory.Core.Categories. Require Import UniMath.CategoryTheory.Core.Isos. Require Import UniMath.CategoryTheory.Core.NaturalTransformations. Require Import UniMath.CategoryTheory.Core.Functors. Require Import UniMath.CategoryTheory.FunctorCategory. Require Import UniMath.CategoryTheory.whiskering.