∀ {k G : Type u} [inst : CommRing k] [inst_1 : Group G] (A : Rep k G),
  groupCohomology.d₁₂ A =
    ModuleCat.ofHom { toFun := fun f g => (A.ρ g.1) (f g.2) - f (g.1 * g.2) + f g.1, map_add' := ⋯, map_smul' := ⋯ }