∀ {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),
  ModuleCat.Hom.hom (groupHomology.mapCycles₂ f φ) = (ModuleCat.Hom.hom (groupHomology.chainsMap₂ f φ)).restrict ⋯