∀ {C : Type u_2} [inst : CategoryTheory.Category.{u_1, u_2} C] [inst_1 : CategoryTheory.Preadditive C]
  (K L : CochainComplex C ℤ) (n m : ℤ) (hm : n + 1 = m) (s : CategoryTheory.Limits.Fork ((K.HomComplex L).d n m) 0),
  CategoryTheory.CategoryStruct.comp
      ((fun s =>
          AddCommGrpCat.ofHom
            { toFun := fun x => ⟨(CategoryTheory.ConcreteCategory.hom s.ι) x, ⋯⟩, map_zero' := ⋯, map_add' := ⋯ })
        s)
      (CategoryTheory.Limits.Fork.ι
        (CategoryTheory.Limits.KernelFork.ofι
          (AddCommGrpCat.ofHom (CochainComplex.HomComplex.Cocycle.toCochainAddMonoidHom K L n)) ⋯)) =
    s.ι