∀ (k : Type u_1) {G : Type u_1} [inst : CommRing k] [inst_1 : Group G] (S : Subgroup G) [inst_2 : S.Normal] (n : ℕ)
  {X Y : Rep k G} (φ : X ⟶ Y),
  CategoryTheory.CategoryStruct.comp
      (((Rep.quotientToInvariantsFunctor k S).comp (groupCohomology.functor k (G ⧸ S) n)).map φ)
      (groupCohomology.map (QuotientGroup.mk' S)
        (Y.subtype (Representation.invariants (MonoidHom.comp Y.ρ S.subtype)) ⋯) n) =
    CategoryTheory.CategoryStruct.comp
      (groupCohomology.map (QuotientGroup.mk' S)
        (X.subtype (Representation.invariants (MonoidHom.comp X.ρ S.subtype)) ⋯) n)
      ((groupCohomology.functor k G n).map φ)