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