  The number and the location of monopoles in Lattice configurations depend on
the choice of the gauge, in contrast to the obvious requirement that monopoles,
as physical objects, have a gauge-invariant status.
  It is proved, starting from non-abelian Bianchi identities, that monopoles
are indeed gauge-invariant: the technique used to detect them has instead an
efficiency which depends on the choice of the abelian projection, in a known
and well understood way.
