{R : Type u} →
  [inst : CommRing R] →
    (weight : Type v) →
      [weightIsAddCommGroup : AddCommGroup weight] →
        [weightIsModule : Module R weight] →
          (coweight : Type v) →
            [coweightIsAddCommGroup : AddCommGroup coweight] →
              [coweightIsModule : Module R coweight] →
                (index : Type v) → RootPairing index R weight coweight → RootPairingCat R