∀ {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
    ((CategoryTheory.presheafToSheaf J AddCommGrpCat).obj ((CategoryTheory.yoneda.obj S.X₂).comp AddCommGrpCat.free))
    ((CategoryTheory.presheafToSheaf J AddCommGrpCat).obj ((CategoryTheory.yoneda.obj S.X₃).comp AddCommGrpCat.free))