Definition PreSheaf_Monic_components_Monic_Monic :
    Monic (F _o c)%object (G _o c)%object
    :=
      {|
        mono_morphism := Trans (mono_morphism N) c;
        mono_morphism_monomorphic :=
          PreSheaf_Monic_components_is_Monic
      |}.

Theorem PreSheaf_Epic_components_is_Epic : g = h.