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