∀ {C : Type u_1} [inst : CategoryTheory.Category.{u_2, u_1} C] {J : CategoryTheory.GrothendieckTopology C}
  [inst_1 : CategoryTheory.HasWeakSheafify J (Type u_2)] [inst_2 : CategoryTheory.HasSheafify J AddCommGrpCat]
  (S : J.MayerVietorisSquare),
  CategoryTheory.Limits.HasBinaryBiproduct
    (S.map
        (CategoryTheory.yoneda.comp
          (((CategoryTheory.Functor.whiskeringRight Cᵒᵖ (Type u_2) AddCommGrpCat).obj AddCommGrpCat.free).comp
            (CategoryTheory.presheafToSheaf J AddCommGrpCat)))).X₂
    (S.map
        (CategoryTheory.yoneda.comp
          (((CategoryTheory.Functor.whiskeringRight Cᵒᵖ (Type u_2) AddCommGrpCat).obj AddCommGrpCat.free).comp
            (CategoryTheory.presheafToSheaf J AddCommGrpCat)))).X₃