∀ {J : Type v} [inst : CategoryTheory.Category.{w, v} J] (F : CategoryTheory.Functor J AddMonCat)
  [inst_1 : Small.{u, max u v} ↑(F.comp (CategoryTheory.forget AddMonCat)).sections] (j : J),
  AddMonCat.limitπAddMonoidHom F j =
    { toFun := (CategoryTheory.Limits.Types.Small.limitCone (F.comp (CategoryTheory.forget AddMonCat))).π.app j,
      map_zero' := ⋯, map_add' := ⋯ }