{C : Type u} →
  [inst : CategoryTheory.Category.{v, u} C] →
    {F :
        CategoryTheory.Pseudofunctor (CategoryTheory.LocallyDiscrete Cᵒᵖ)
          (CategoryTheory.Bicategory.Adj CategoryTheory.Cat)} →
      {ι : Type t} →
        {S : C} →
          {X : ι → C} →
            {f : (i : ι) → X i ⟶ S} →
              {D₁ D₂ : F.DescentDataAsCoalgebra f} →
                (hom : (i : ι) → D₁.obj i ⟶ D₂.obj i) →
                  autoParam
                      (∀ (i₁ i₂ : ι),
                        CategoryTheory.CategoryStruct.comp (D₁.hom i₁ i₂)
                            ((F.map (f i₁).op.toLoc).l.toFunctor.map
                              ((F.map (f i₂).op.toLoc).r.toFunctor.map (hom i₂))) =
                          CategoryTheory.CategoryStruct.comp (hom i₁) (D₂.hom i₁ i₂))
                      CategoryTheory.Pseudofunctor.DescentDataAsCoalgebra.Hom.comm._autoParam →
                    D₁.Hom D₂