def super_categories(self):
"""
EXAMPLES::
sage: Coalgebras(QQ).super_categories()
[Category of vector spaces over Rational Field]
"""
return [Modules(self.base_ring())]
def super_categories(self):
"""
EXAMPLES::
sage: GradedModules(QQ).super_categories()
[Category of vector spaces over Rational Field]
sage: GradedModules(ZZ).super_categories()
[Category of modules over Integer Ring]
"""
R = self.base_ring()
return [Modules(R)]
def super_categories(self):
"""
EXAMPLES::
sage: ChainComplexes(Integers(9)).super_categories()
[Category of modules over Ring of integers modulo 9]
"""
from sage.categories.all import Fields, Modules, VectorSpaces
base_ring = self.base_ring()
if base_ring in Fields():
return [VectorSpaces(base_ring)]
return [Modules(base_ring)]
def category_meet(self, other):
"""
TESTS::
sage: from yacop.categories.utils import category_meet
sage: from yacop.categories.left_modules import YacopLeftModules
sage: from yacop.categories.right_modules import YacopRightModules
sage: A3=YacopLeftModules(SteenrodAlgebra(3))
sage: category_meet(A3,A3)
Category of yacop left modules over mod 3 Steenrod algebra, milnor basis
sage: category_meet(A3,Modules(GF(3)))
Category of vector spaces over Finite Field of size 3
sage: A2=YacopLeftModules(SteenrodAlgebra(2))
sage: B2=YacopLeftModules(SteenrodAlgebra(2,profile=(2,1,1)))
sage: category_meet(A2,B2)
Category of yacop left modules over sub-Hopf algebra of mod 2 Steenrod algebra, milnor basis, profile function [2, 1, 1]
sage: A2=YacopRightModules(SteenrodAlgebra(2))
sage: B2=YacopRightModules(SteenrodAlgebra(2,profile=(2,1,1)))
sage: category_meet(A2,B2)
Category of yacop right modules over sub-Hopf algebra of mod 2 Steenrod algebra, milnor basis, profile function [2, 1, 1]
"""
import yacop.categories
oR = other.base_ring()
B = steenrod_algebra_intersect((self.base_ring(), oR))
if not hasattr(B, "is_generic"):
return Modules(FiniteField(B.characteristic()))
is_algebra = self._yacop_has_multiplication() and other._yacop_has_multiplication()
is_right = self._yacop_has_right_action() and other._yacop_has_right_action()
is_left = self._yacop_has_left_action() and other._yacop_has_left_action()
is_bimod = is_left and is_right
if is_algebra:
if is_bimod:
return yacop.categories.bimodules.YacopBimoduleAlgebras(B)
elif is_right:
return yacop.categories.right_modules.YacopRightModuleAlgebras(B)
else:
return yacop.categories.left_modules.YacopLeftModuleAlgebras(B)
else:
if is_bimod:
return yacop.categories.bimodules.YacopBimodules(B)
elif is_right:
return yacop.categories.right_modules.YacopRightModules(B)
else:
return yacop.categories.left_modules.YacopLeftModules(B)
def __init__(self, X, Y, category=None):
"""
EXAMPLES::
sage: V = span([[1/2,1,1],[3/2,2,1],[0,0,1]],ZZ); W = V.span([2*V.0+4*V.1, 9*V.0+12*V.1, 4*V.2]); Q = V/W
sage: type(Q.Hom(Q))
<class 'sage.modules.fg_pid.fgp_morphism.FGP_Homset_class_with_category'>
"""
if category is None:
from sage.modules.free_module import is_FreeModule
if is_FreeModule(X) and is_FreeModule(Y):
from sage.categories.all import FreeModules
category = FreeModules(X.base_ring())
else:
from sage.categories.all import Modules
category = Modules(X.base_ring())
Homset.__init__(self, X, Y, category)