  We prove that the class of Gorenstein injective modules is covering if and
only if it is closed under direct limits. This adds to the list of examples
that support Enochs conjecture: Every covering class of modules is closed under
direct limits.
  We also show that the class of Gorenstein injective left R-modules is
covering if and only if R is left noetherian, and such that character modules
of Gorenstein injective left R modules are Gorenstein flat.
