∀ {C : Type u_1} [inst : CategoryTheory.Category.{v_1, u_1} C] [inst_1 : CategoryTheory.Limits.HasZeroMorphisms C]
  {X Y : C} (f : X ⟶ Y) (Z : C) [CategoryTheory.Limits.HasCokernel f],
  { X₁ := X, X₂ := Y, X₃ := Z, f := f, g := 0, zero := ⋯ }.HasLeftHomology