∀ {k G : Type u} [inst : CommRing k] [inst_1 : Group G] (A : Rep k G) {Z : ModuleCat k} (h : groupHomology.H0 A ⟶ Z),
  CategoryTheory.CategoryStruct.comp (groupHomology.cyclesIso₀ A).hom
      (CategoryTheory.CategoryStruct.comp (groupHomology.H0π A) h) =
    CategoryTheory.CategoryStruct.comp (groupHomology.π A 0) h