{C : Type u₁} →
  [inst : CategoryTheory.Category.{v₁, u₁} C] →
    {D : Type u₂} →
      [inst_1 : CategoryTheory.Category.{v₂, u₂} D] →
        {S : CategoryTheory.Functor C D} →
          {T : D} →
            [CategoryTheory.Limits.HasFiniteColimits C] →
              [CategoryTheory.Limits.PreservesFiniteColimits S] →
                (A : CategoryTheory.CostructuredArrow S T) →
                  CategoryTheory.Subobject (Opposite.op A) ≃o
                    { P // ∃ q, CategoryTheory.CategoryStruct.comp (S.map P.arrow.unop) q = A.hom }