∀ {k G : Type u} [inst : CommRing k] [inst_1 : CommGroup G] [inst_2 : Fintype G] (A : Rep k G) (g : G)
  (hg : ∀ (x : G), x ∈ Subgroup.zpowers g) (i : ℕ) (hi : Odd i) (x : ↥(ModuleCat.Hom.hom A.norm.hom).ker),
  (CategoryTheory.ConcreteCategory.hom (Rep.FiniteCyclicGroup.groupCohomologyπOdd A g hg i hi)) x = 0 ↔
    ↑x ∈ (ModuleCat.Hom.hom (A.applyAsHom g - CategoryTheory.CategoryStruct.id A).hom).range