proposition: Lemma fully_faithful_conservative {C D : category} (F : functor C D) (FF : fully_faithful F) : conservative F.
proof: Proof. unfold conservative. intros a b f is_iso_Ff. use transportf. - exact (FF^-1 (# F f)). - apply fully_faithful_inv_hom_is_inv. - apply (fully_faithful_reflects_iso_proof _ _ _ _ _ _ (_,,is_iso_Ff)). Defined.
imports: UniMath.Foundations.PartD UniMath.Foundations.Propositions UniMath.Foundations.Sets UniMath.MoreFoundations.PartA UniMath.MoreFoundations.Univalence UniMath.MoreFoundations.Tactics UniMath.CategoryTheory.Core.Categories UniMath.CategoryTheory.Core.Isos UniMath.CategoryTheory.Core.TransportMorphisms UniMath.CategoryTheory.Core.Univalence