∀ {k G H : Type u} [inst : CommRing k] [inst_1 : Group G] [inst_2 : Group H] {A : Rep k H} {B : Rep k G} (f : G →* H)
  (φ : (Action.res (ModuleCat k) f).obj A ⟶ B),
  CategoryTheory.CategoryStruct.comp ((groupCohomology.cochainsMap f φ).f 2) (groupCohomology.cochainsIso₂ B).hom =
    CategoryTheory.CategoryStruct.comp (groupCohomology.cochainsIso₂ A).hom (groupCohomology.cochainsMap₂ f φ)