Made it so you must explicitly designate graded as a super category

src/sage/algebras/clifford_algebra.py

@@ -1412,7 +1412,8 @@ def __init__(self, R, names):
             sage: E.<x,y,z> = ExteriorAlgebra(QQ)
             sage: TestSuite(E).run()
         """
-        CliffordAlgebra.__init__(self, QuadraticForm(R, len(names)), names, HopfAlgebrasWithBasis(R).Super())
+        cat = HopfAlgebrasWithBasis(R).Super().Graded()
+        CliffordAlgebra.__init__(self, QuadraticForm(R, len(names)), names, cat)
         # TestSuite will fail if the HopfAlgebra classes will ever have tests for
         # the coproduct being an algebra morphism -- since this is really a
         # Hopf superalgebra, not a Hopf algebra.

src/sage/categories/hopf_algebras_with_basis.py

@@ -146,6 +146,7 @@ def example(self, G = None):
 
     FiniteDimensional = LazyImport('sage.categories.finite_dimensional_hopf_algebras_with_basis', 'FiniteDimensionalHopfAlgebrasWithBasis')
     Graded = LazyImport('sage.categories.graded_hopf_algebras_with_basis', 'GradedHopfAlgebrasWithBasis')
+    Super = LazyImport('sage.categories.super_hopf_algebras_with_basis',  'SuperHopfAlgebrasWithBasis')
 
     class ParentMethods:
 

src/sage/categories/super_algebras.py

@@ -9,6 +9,9 @@
 #******************************************************************************
 
 from sage.categories.super_modules import SuperModulesCategory
+from sage.categories.algebras import Algebras
+from sage.categories.modules import Modules
+from sage.misc.lazy_import import LazyImport
 
 class SuperAlgebras(SuperModulesCategory):
     """
@@ -18,14 +21,22 @@ class SuperAlgebras(SuperModulesCategory):
 
         sage: Algebras(ZZ).Super()
         Category of super algebras over Integer Ring
-        sage: Algebras(ZZ).Super().super_categories()
-        [Category of graded algebras over Integer Ring,
-         Category of super modules over Integer Ring]
 
     TESTS::
 
         sage: TestSuite(Algebras(ZZ).Super()).run()
     """
+    def super_categories(self):
+        """
+        EXAMPLES::
+
+            sage: Algebras(ZZ).Super().super_categories()
+            [Category of graded algebras over Integer Ring,
+             Category of super modules over Integer Ring]
+        """
+        R = self.base_ring()
+        return [Algebras(R).Graded(), Modules(R).Super()]
+
     class ParentMethods:
         pass
 

src/sage/categories/super_algebras_with_basis.py

@@ -9,6 +9,8 @@
 #******************************************************************************
 
 from sage.categories.super_modules import SuperModulesCategory
+from sage.categories.algebras import Algebras
+from sage.categories.modules import Modules
 
 class SuperAlgebrasWithBasis(SuperModulesCategory):
     """
@@ -20,13 +22,24 @@ class SuperAlgebrasWithBasis(SuperModulesCategory):
         Category of super algebras with basis over Integer Ring
         sage: sorted(C.super_categories(), key=str)
         [Category of graded algebras with basis over Integer Ring,
-         Category of super algebras over Integer Ring,
          Category of super modules with basis over Integer Ring]
 
     TESTS::
 
         sage: TestSuite(C).run()
     """
+    def super_categories(self):
+        """
+        EXAMPLES::
+
+            sage: Algebras(ZZ).WithBasis().Super().super_categories()
+            [Category of graded algebras with basis over Integer Ring,
+             Category of super modules with basis over Integer Ring]
+        """
+        R = self.base_ring()
+        return [Algebras(R).WithBasis().Graded(),
+                Modules(R).WithBasis().Super()]
+
     class ParentMethods:
         pass
 

src/sage/categories/super_hopf_algebras_with_basis.py

@@ -0,0 +1,35 @@
+r"""
+Super algebras with basis
+"""
+#*****************************************************************************
+#  Copyright (C) 2015 Travis Scrimshaw <tscrim at ucdavis.edu>
+#
+#  Distributed under the terms of the GNU General Public License (GPL)
+#                  http://www.gnu.org/licenses/
+#******************************************************************************
+
+from sage.categories.super_modules import SuperModulesCategory
+
+class SuperHopfAlgebrasWithBasis(SuperModulesCategory):
+    """
+    The category of super algebras with a distinguished basis
+
+    EXAMPLES::
+
+        sage: C = HopfAlgebras(ZZ).WithBasis().Super(); C
+        Category of super hopf algebras with basis over Integer Ring
+        sage: sorted(C.super_categories(), key=str)
+        [Category of hopf algebras with basis over Integer Ring,
+         Category of super algebras over Integer Ring,
+         Category of super algebras with basis over Integer Ring]
+
+    TESTS::
+
+        sage: TestSuite(C).run()
+    """
+    class ParentMethods:
+        pass
+
+    class ElementMethods:
+        pass
+

src/sage/categories/super_modules.py

@@ -124,31 +124,6 @@ def _repr_object_names(self):
         """
         return "super {}".format(self.base_category()._repr_object_names())
 
-    @classmethod
-    def default_super_categories(cls, category, *args):
-        """
-        Returns the default super categories of ``category.Subobjects()``
-
-        Mathematical meaning: if `A` is a super version of `B`,
-        then `A` is also a graded version of `B`.
-
-        INPUT:
-
-         - ``cls`` -- the class ``SubobjectsCategory``
-         - ``category`` -- a category `Cat`
-
-        OUTPUT: a (join) category
-
-        In practice, this returns ``category.Subquotients()``, joined
-        together with the result of the method
-        :meth:`RegressiveCovariantConstructionCategory.default_super_categories() <sage.categories.covariant_functorial_construction.RegressiveCovariantConstructionCategory.default_super_categories>`
-        (that is the join of ``category`` and ``cat.Subobjects()`` for
-        each ``cat`` in the super categories of ``category``).
-
-        EXAMPLES::
-        """
-        return Category.join([category.Graded(), super(SuperModulesCategory, cls).default_super_categories(category, *args)])
-
 class SuperModules(SuperModulesCategory):
     """
     The category of super modules.
@@ -170,6 +145,22 @@ class SuperModules(SuperModulesCategory):
 
         sage: TestSuite(Modules(ZZ).Super()).run()
     """
+    def super_categories(self):
+        """
+        EXAMPLES::
+
+            sage: Modules(ZZ).Super().super_categories()
+            [Category of graded modules over Integer Ring]
+
+        Nota bene::
+
+            sage: Modules(QQ).Super()
+            Category of super modules over Rational Field
+            sage: Modules(QQ).Super().super_categories()
+            [Category of graded modules over Rational Field]
+        """
+        return [Modules(self.base_ring()).Graded()]
+
     def extra_super_categories(self):
         r"""
         Adds :class:`VectorSpaces` to the super categories of ``self`` if