∀ {k : Type u_1} [inst : CommRing k] {G : Type u_2} [inst_1 : Group G] (A B C : Rep.{u_1, u_1, u_2} k G)
  (f : CategoryTheory.MonoidalCategoryStruct.tensorObj A B ⟶ C) (g : G),
  (TensorProduct.curry (Rep.Hom.hom f).toLinearMap).flip ∘ₗ B.ρ g =
    (A.ρ.linHom C.ρ) g ∘ₗ (TensorProduct.curry (Rep.Hom.hom f).toLinearMap).flip