{C : Type u} →
  [inst : CategoryTheory.Category.{v, u} C] →
    {D : Type u₁} →
      [inst_1 : CategoryTheory.Category.{v₁, u₁} D] →
        (F : CategoryTheory.Functor C CategoryTheory.Cat) →
          (G : D ≌ C) →
            CategoryTheory.Functor (CategoryTheory.Grothendieck F) (CategoryTheory.Grothendieck (G.functor.comp F))