∀ {ι : Type u_3} {W₁ : Type u_5} {W₂ : Type u_1} [inst : CategoryTheory.Category.{u_4, u_5} W₁]
  [inst_1 : CategoryTheory.Category.{u_2, u_1} W₂] [inst_2 : CategoryTheory.Limits.HasZeroMorphisms W₁]
  [inst_3 : CategoryTheory.Limits.HasZeroMorphisms W₂] [inst_4 : CategoryTheory.Limits.HasZeroObject W₁]
  [inst_5 : CategoryTheory.Limits.HasZeroObject W₂] (F : CategoryTheory.Functor W₁ W₂)
  [inst_6 : F.PreservesZeroMorphisms] (c : ComplexShape ι) [inst_7 : DecidableEq ι] (j : ι) (X : W₁) (i : ι),
  i = j →
    ((F.comp (HomologicalComplex.single W₂ c j)).obj X).X i =
      (((HomologicalComplex.single W₁ c j).comp (F.mapHomologicalComplex c)).obj X).X i