proposition: Lemma faithful_reflects_epis {C D:precategory} (U:functor C D) (hU:faithful U) {a b:C} (f:C⟦a,b⟧) : isEpi (#U f) -> isEpi f.
proof: Proof. intros hf c u v huv. eapply invmaponpathsincl. apply hU. cbn. apply hf. rewrite <- functor_comp, <- functor_comp. now rewrite huv. Qed.
imports: UniMath.Foundations.PartD UniMath.Foundations.Propositions UniMath.Foundations.Sets UniMath.MoreFoundations.Tactics UniMath.CategoryTheory.Core.Categories UniMath.CategoryTheory.Core.Isos UniMath.CategoryTheory.Core.Functors UniMath.CategoryTheory.Core.NaturalTransformations UniMath.CategoryTheory.Epis UniMath.CategoryTheory.FunctorCategory UniMath.CategoryTheory.Limits.Graphs.Pullbacks UniMath.CategoryTheory.Limits.Graphs.Limits UniMath.CategoryTheory.Limits.Graphs.Colimits UniMath.CategoryTheory.Limits.Graphs.Coequalizers UniMath.CategoryTheory.Limits.Pullbacks UniMath.CategoryTheory.Limits.Graphs.Pushouts UniMath.CategoryTheory.Limits.Graphs.EqDiag UniMath.CategoryTheory.Limits.Pushouts UniMath.CategoryTheory.Limits.Coequalizers