∀ {C : Type u} [inst : CategoryTheory.Category.{v, u} C] [inst_1 : CategoryTheory.IsCofilteredOrEmpty C] {α : Type w}
  (f : α → C),
  CategoryTheory.EssentiallySmall.{max v w, v, u} (CategoryTheory.IsCofiltered.cofilteredClosure f).FullSubcategory