∀ {k G : Type u} [inst : CommRing k] [inst_1 : Group G] (A : Rep.{max u u_1, u, u} k G),
  groupCohomology.shortComplexH1 A =
    { X₁ := ModuleCat.of k ↑A, X₂ := ModuleCat.of k (G → ↑A), X₃ := ModuleCat.of k (G × G → ↑A),
      f := groupCohomology.d₀₁ A, g := groupCohomology.d₁₂ A, zero := ⋯ }