Sort u →
  {B : Type u_1} →
    {C : Type u_2} →
      [inst : CategoryTheory.Bicategory C] →
        {F : B → C} →
          {X Y : CategoryTheory.Bicategory.InducedBicategory C F} →
            {f g : X ⟶ Y} →
              CategoryTheory.Bicategory.InducedBicategory.Hom₂ f g →
                {B' : Type u_1} →
                  {C' : Type u_2} →
                    [inst' : CategoryTheory.Bicategory C'] →
                      {F' : B' → C'} →
                        {X' Y' : CategoryTheory.Bicategory.InducedBicategory C' F'} →
                          {f' g' : X' ⟶ Y'} → CategoryTheory.Bicategory.InducedBicategory.Hom₂ f' g' → Sort u