∀ (C : Type u_1) [inst : CategoryTheory.Category.{v_1, u_1} C] [inst_1 : CategoryTheory.Preadditive C]
  [CategoryTheory.Limits.HasBinaryBiproducts C] [inst_3 : CategoryTheory.CategoryWithHomology C],
  (ComplexShape.up ℤ).QFactorsThroughHomotopy C