∀ {k G : Type u} [inst : CommRing k] [inst_1 : Group G] (A : Rep k G) {Z : ModuleCat k}
  (h : (groupCohomology.inhomogeneousCochains A).X 0 ⟶ Z),
  CategoryTheory.CategoryStruct.comp (groupCohomology.cocyclesIso₀ A).inv
      (CategoryTheory.CategoryStruct.comp (groupCohomology.iCocycles A 0) h) =
    CategoryTheory.CategoryStruct.comp (groupCohomology.shortComplexH0 A).f
      (CategoryTheory.CategoryStruct.comp (groupCohomology.cochainsIso₀ A).inv h)