proposition: Lemma pre_composition_with_ess_surj_and_full_is_full_and_faithful : full_and_faithful (pre_composition_functor A B C H).
proof: Proof. split. apply pre_composition_with_ess_surj_and_full_is_full. apply pre_composition_with_ess_surj_is_faithful. assumption. Defined.
imports: UniMath.Foundations.PartD UniMath.Foundations.Propositions UniMath.Foundations.Sets UniMath.CategoryTheory.Core.Categories UniMath.CategoryTheory.Core.Isos UniMath.CategoryTheory.Core.NaturalTransformations UniMath.CategoryTheory.Core.Functors UniMath.CategoryTheory.FunctorCategory UniMath.CategoryTheory.whiskering