∀ {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] {X Y Z : CategoryTheory.ShortComplex C} (f : X ⟶ Y) (g : Y ⟶ Z),
  { τ₁ := F.map (CategoryTheory.CategoryStruct.comp f g).τ₁, τ₂ := F.map (CategoryTheory.CategoryStruct.comp f g).τ₂,
      τ₃ := F.map (CategoryTheory.CategoryStruct.comp f g).τ₃, comm₁₂ := ⋯, comm₂₃ := ⋯ } =
    CategoryTheory.CategoryStruct.comp
      { τ₁ := F.map f.τ₁, τ₂ := F.map f.τ₂, τ₃ := F.map f.τ₃, comm₁₂ := ⋯, comm₂₃ := ⋯ }
      { τ₁ := F.map g.τ₁, τ₂ := F.map g.τ₂, τ₃ := F.map g.τ₃, comm₁₂ := ⋯, comm₂₃ := ⋯ }