proposition: Lemma faithful_reflects_mono {C D : category} (F : functor C D) (FF : faithful F) : reflects_morphism F (@isMonic).
proof: Proof. unfold reflects_morphism. intros ? ? ? is_monic_Ff. intros ? ? ? eqcomp. apply (Injectivity (# F)). - apply isweqonpathsincl, FF. - apply is_monic_Ff. refine (!(functor_comp F g f) @ _). refine (_ @ functor_comp F h f). apply maponpaths; 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.FunctorCategory UniMath.CategoryTheory.Subcategory.Core UniMath.CategoryTheory.Core.Functors