  The hole argument was developed by Einstein in 1913 while he was searching
for a relativistic theory of gravitation. Einstein used the language of
coordinate systems and coordinate invariance, rather than the language of
manifolds and diffeomorphism invariance. He formulated the hole argument
against covariant field equations and later found a way to avoid it using
coordinate language.
  In this paper we shall use the invariant language of categories, manifolds
and natural objects to give a coordinate-free description of the hole argument
and a way of avoiding it. Finally we shall point out some important
implications of further extensions of the hole argument to sets and relations
for the problem of quantum gravity.
