∀ {C : Type u_2} {D : Type u_4} [inst : CategoryTheory.Category.{u_1, u_2} C]
  [inst_1 : CategoryTheory.Category.{u_3, u_4} D] [inst_2 : CategoryTheory.Limits.HasZeroMorphisms C]
  [inst_3 : CategoryTheory.Limits.HasZeroMorphisms D] (F : CategoryTheory.Functor C D)
  [inst_4 : F.PreservesZeroMorphisms] [inst_5 : CategoryTheory.Limits.HasKernels C]
  [inst_6 : CategoryTheory.Limits.HasCokernels C] [inst_7 : F.PreservesHomology] {X Y : CategoryTheory.ShortComplex C}
  (f : X ⟶ Y),
  CategoryTheory.CategoryStruct.comp (CategoryTheory.ShortComplex.cyclesMap (F.mapShortComplex.map f))
      (Y.mapCyclesIso F).hom =
    CategoryTheory.CategoryStruct.comp (X.mapCyclesIso F).hom (F.map (CategoryTheory.ShortComplex.cyclesMap f))