∀ {k G : Type u_1} [inst : CommRing k] [inst_1 : Group G] (A : Rep.{u_1, u_1, u_1} k G),
  AddMonoidHomClass (↑(groupHomology.H1 A) →ₗ[k] ↑(groupHomology.shortComplexH1 A).moduleCatLeftHomologyData.H)
    ↑(groupHomology.H1 A) ↑(groupHomology.shortComplexH1 A).moduleCatLeftHomologyData.H