sage: Q = RootSystem(['A',3]).root_space(GF(3))
sage: W = WeylGroup(['A',3], prefix='s')
sage: cartesian_product([W, Q])
The Cartesian product of (Weyl Group of type ['A', 3] (as a matrix group acting on the ambient space), Root space over the Finite Field of size 3 of the Root system of type ['A', 3])
sage: cartesian_product([Q, W])
---------------------------------------------------------------------------
KeyError                                  Traceback (most recent call last)
File ~/sage/src/sage/misc/cachefunc.pyx:1019, in sage.misc.cachefunc.CachedFunction.__call__()
   1018 try:
-> 1019     return self.cache[k]
   1020 except TypeError:  # k is not hashable

File ~/sage/src/sage/misc/weak_dict.pyx:709, in sage.misc.weak_dict.WeakValueDictionary.__getitem__()
    708 if wr == NULL:
--> 709     raise KeyError(k)
    710 out = PyWeakref_GetObject(wr)

KeyError: ((<class 'sage.combinat.free_module.CombinatorialFreeModule_CartesianProduct'>, (Root space over the Finite Field of size 3 of the Root system of type ['A', 3], Weyl Group of type ['A', 3] (as a matrix group acting on the ambient space))), (('category', Category of Cartesian products of sets),))

During handling of the above exception, another exception occurred:

KeyError                                  Traceback (most recent call last)
File ~/sage/src/sage/structure/category_object.pyx:857, in sage.structure.category_object.CategoryObject.getattr_from_category()
    856 try:
--> 857     return self._cached_methods[name]
    858 except KeyError:

KeyError: 'basis'

During handling of the above exception, another exception occurred:

AttributeError                            Traceback (most recent call last)
Cell In[17], line 1
----> 1 cartesian_product([Q, W])

File ~/sage/src/sage/categories/cartesian_product.py:194, in CartesianProductFunctor.__call__(self, args, **kwds)
    191 elif self._forced_category is not None:
    192     return super().__call__(args, category=self._forced_category, **kwds)
--> 194 return super().__call__(args, **kwds)

File ~/sage/src/sage/categories/covariant_functorial_construction.py:226, in CovariantFunctorialConstruction.__call__(self, args, **kwargs)
    224 assert all(hasattr(arg, self._functor_name) for arg in args)
    225 assert len(args) > 0
--> 226 return getattr(args[0], self._functor_name)(*args[1:], **kwargs)

File ~/sage/src/sage/categories/sets_cat.py:1601, in Sets.ParentMethods.cartesian_product(*parents, **kwargs)
   1599     else:
   1600         category = category & extra_category
-> 1601 return parents[0].CartesianProduct(parents, category=category, **kwargs)

File ~/sage/src/sage/misc/classcall_metaclass.pyx:321, in sage.misc.classcall_metaclass.ClasscallMetaclass.__call__()
    319 """
    320 if cls.classcall is not None:
--> 321     return cls.classcall(cls, *args, **kwds)
    322 else:
    323     # Fast version of type.__call__(cls, *args, **kwds)

File ~/sage/src/sage/misc/cachefunc.pyx:1024, in sage.misc.cachefunc.CachedFunction.__call__()
   1022         return self.cache[k]
   1023 except KeyError:
-> 1024     w = self.f(*args, **kwds)
   1025     self.cache[k] = w
   1026     return w

File ~/sage/src/sage/structure/unique_representation.py:1113, in CachedRepresentation.__classcall__(cls, *args, **options)
   1098 @weak_cached_function(cache=128)  # automatically a staticmethod
   1099 def __classcall__(cls, *args, **options):
   1100     """
   1101     Construct a new object of this class or reuse an existing one.
   1102 
   (...)
   1111         True
   1112     """
-> 1113     return super().__classcall__(cls, *args, **options)

File ~/sage/src/sage/structure/unique_representation.py:597, in WithPicklingByInitArgs.__classcall__(cls, *args, **options)
    573 @staticmethod
    574 def __classcall__(cls, *args, **options):
    575     """
    576     Construct a new object of this class and store the arguments passed to ``__init__``.
    577 
   (...)
    595         False
    596     """
--> 597     instance = typecall(cls, *args, **options)
    598     assert isinstance(instance, cls)
    599     if instance.__class__.__reduce__ == WithPicklingByInitArgs.__reduce__:

File ~/sage/src/sage/misc/classcall_metaclass.pyx:472, in sage.misc.classcall_metaclass.typecall()
    470     2
    471 """
--> 472 return (<PyTypeObject*>type).tp_call(cls, args, kwds)
    473 
    474 

File ~/sage/src/sage/combinat/free_module.py:1797, in CombinatorialFreeModule_CartesianProduct.__init__(self, modules, **options)
   1793 # should check the base ring
   1794 self._sets = modules
   1795 CombinatorialFreeModule.__init__(self, R,
   1796     DisjointUnionEnumeratedSets(
-> 1797         [module.basis().keys() for module in modules], keepkey=True),
   1798     **options)

File ~/sage/src/sage/structure/category_object.pyx:851, in sage.structure.category_object.CategoryObject.__getattr__()
    849         AttributeError: 'PrimeNumbers_with_category' object has no attribute 'sadfasdf'...
    850     """
--> 851     return self.getattr_from_category(name)
    852 
    853 cdef getattr_from_category(self, name):

File ~/sage/src/sage/structure/category_object.pyx:866, in sage.structure.category_object.CategoryObject.getattr_from_category()
    864     cls = self._category.parent_class
    865 
--> 866 attr = getattr_from_other_class(self, cls, name)
    867 self._cached_methods[name] = attr
    868 return attr

File ~/sage/src/sage/cpython/getattr.pyx:358, in sage.cpython.getattr.getattr_from_other_class()
    356     dummy_error_message.cls = type(self)
    357     dummy_error_message.name = name
--> 358     raise AttributeError(dummy_error_message)
    359 cdef PyObject* attr = instance_getattr(cls, name)
    360 if attr is NULL:

AttributeError: 'WeylGroup_gens_with_category' object has no attribute 'basis'