∀ {ι : Type u_1} {V : Type u_3} [inst : CategoryTheory.Category.{u_2, u_3} V]
  [inst_1 : CategoryTheory.Limits.HasZeroMorphisms V] {c : ComplexShape ι} {C₁ C₂ : HomologicalComplex V c}
  (f : (i : ι) → C₁.X i ≅ C₂.X i)
  (hf :
    ∀ (i j : ι),
      c.Rel i j →
        CategoryTheory.CategoryStruct.comp (f i).hom (C₂.d i j) =
          CategoryTheory.CategoryStruct.comp (C₁.d i j) (f j).hom),
  CategoryTheory.CategoryStruct.comp { f := fun i => (f i).hom, comm' := hf } { f := fun i => (f i).inv, comm' := ⋯ } =
    CategoryTheory.CategoryStruct.id C₁