∀ {k G : Type u} [inst : CommRing k] [inst_1 : Group G] (A : Rep k G),
  groupCohomology.H2Iso A =
    (HomologicalComplex.sc (groupCohomology.inhomogeneousCochains A) 2).leftHomologyIso.symm ≪≫
      CategoryTheory.ShortComplex.leftHomologyMapIso' (groupCohomology.isoShortComplexH2 A)
        (HomologicalComplex.sc (groupCohomology.inhomogeneousCochains A) 2).leftHomologyData
        (groupCohomology.shortComplexH2 A).moduleCatLeftHomologyData