∀ {X Y Z : CommGrpCatᵒᵖ} (f : X ⟶ Y) (g : Y ⟶ Z),
  { app := fun N => CommGrpCat.ofHom (CommGrpCat.Hom.hom (CategoryTheory.CategoryStruct.comp f g).unop).compHom',
      naturality := ⋯ } =
    CategoryTheory.CategoryStruct.comp
      { app := fun N => CommGrpCat.ofHom (CommGrpCat.Hom.hom f.unop).compHom', naturality := ⋯ }
      { app := fun N => CommGrpCat.ofHom (CommGrpCat.Hom.hom g.unop).compHom', naturality := ⋯ }