∀ (C : Type u_2) [inst : CategoryTheory.Category.{u_1, u_2} C] [inst_1 : CategoryTheory.Limits.HasZeroMorphisms C]
  {ι : Type u_3} (c : ComplexShape ι) [inst_2 : CategoryTheory.CategoryWithHomology C] (X : HomologicalComplex C c),
  (fun i => HomologicalComplex.homologyMap (CategoryTheory.CategoryStruct.id X) i) =
    CategoryTheory.CategoryStruct.id fun i => X.homology i