  In this paper we review the hole argument for the space-time points and
elementary particles and generalize the hole argument to include all geometric
object fields and diffeomorphisms; and, by application of forgetful functors to
abstract from differentiability and even continuity, the hole argument is
applied to a much wider class of mathematical objects. We discuss the problem
concerning the individuation of the objects in more general settings such that
fibered manifolds, fibered sets and n-ary relations.
