{k : Type u} →
  [inst : CommRing k] →
    {G H : Type u} →
      [inst_1 : Group G] →
        [inst_2 : Group H] →
          (φ : G →* H) →
            (A : Rep.{u, u, u} k G) →
              (B : Rep.{u, u, u} k H) →
                ((Rep.coinvariantsTensor k H).obj (Rep.ind φ A)).obj B ≅
                  ((Rep.coinvariantsTensor k G).obj A).obj (Rep.res φ B)