∀ {k G H : Type u} [inst : CommRing k] [inst_1 : Group G] [inst_2 : Group H] {A : Rep k G} {B : Rep k H} (f : G →* H)
  (φ : A ⟶ (Action.res (ModuleCat k) f).obj B) (n : ℕ) {Z : ModuleCat k} (h : groupHomology B n ⟶ Z),
  CategoryTheory.CategoryStruct.comp (groupHomology.π A n)
      (CategoryTheory.CategoryStruct.comp (groupHomology.map f φ n) h) =
    CategoryTheory.CategoryStruct.comp (groupHomology.cyclesMap f φ n)
      (CategoryTheory.CategoryStruct.comp (groupHomology.π B n) h)