∀ {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),
  CategoryTheory.CategoryStruct.comp (groupHomology.H1π A) (groupHomology.map f φ 1) =
    CategoryTheory.CategoryStruct.comp (groupHomology.mapCycles₁ f φ) (groupHomology.H1π B)