∀ {C : Type u_4} [inst : CategoryTheory.Category.{u_3, u_4} C] {D : Type u_2}
  [inst_1 : CategoryTheory.Category.{u_1, u_2} D] {S : CategoryTheory.Functor C D} {T : D}
  [inst_2 : CategoryTheory.Limits.HasFiniteColimits C] [inst_3 : CategoryTheory.Limits.PreservesFiniteColimits S]
  (A : CategoryTheory.CostructuredArrow S T)
  (P : { P // ∃ q, CategoryTheory.CategoryStruct.comp (S.map P.arrow.unop) q = A.hom }),
  ∃ q,
    CategoryTheory.CategoryStruct.comp
        (S.map
          (CategoryTheory.CostructuredArrow.projectQuotient
                (CategoryTheory.CostructuredArrow.liftQuotient ↑P ⋯)).arrow.unop)
        q =
      A.hom