  We give a direct description of the category of sheaves on Lichtenbaum's
Weil-\'etale site of a number ring. Then we apply this result to define a
spectral sequence relating Weil-\'etale cohomology to Artin-Verdier \'etale
cohomology. Finally we construct complexes of \'etale sheaves computing the
expected Weil-\'etale cohomology.
