def basis(self, region=None):
# this assumes a _basis_walker method in the subquotient object
wk = self._sq._basis_walker(region)
if self._am.graded_basis(region).cardinality() < Infinity:
cat = FiniteEnumeratedSets()
else:
cat = InfiniteEnumeratedSets()
res = Family(wk, lambda i: i, lazy=True)
res._refine_category_(cat)
return res
