∀ {C : Type u_1} [inst : CategoryTheory.Category.{v_1, u_1} C] [inst_1 : CategoryTheory.Abelian C]
  (K : CochainComplex C ℤ) [K.IsKProjective],
  (HomotopyCategory.subcategoryAcyclic C).leftOrthogonal ((HomotopyCategory.quotient C (ComplexShape.up ℤ)).obj K)