def super_categories(self):
"""
EXAMPLES::
sage: PolyhedralSets(QQ).super_categories()
[Category of magmas, Category of additive magmas]
"""
from sage.categories.all import Magmas, AdditiveMagmas
return [Magmas(), AdditiveMagmas()]
def __init__(self, generators):
r"""
TESTS::
sage: sys.path.append(os.getcwd()); from mac_lane import * # optional: standalone
sage: isinstance(DiscreteValueSemigroup([0]), DiscreteValueSemigroup)
True
"""
from sage.categories.all import AdditiveMagmas
self._generators = generators
category = AdditiveMagmas().AdditiveAssociative().AdditiveUnital()
if all([-g in generators for g in generators]):
# check whether this is trivially a group
# is_group() performs a complete check that is very costly and
# refines the category
category = category.AdditiveInverse()
# We can not set the facade to DiscreteValuationCodomain since there
# are some issues with iterated facades currently
Parent.__init__(self, facade=QQ, category=category)