Adding some more stubs for categories.

src/sage/categories/all.py

@@ -3,10 +3,11 @@
 from category_types import(
                         Elements,
                         Sequences,
-                        SimplicialComplexes,
                         ChainComplexes,
 )
 
+from sage.categories.simplicial_complexes import SimplicialComplexes
+
 from tensor     import tensor
 from cartesian_product import cartesian_product
 

src/sage/categories/category_types.py

@@ -599,34 +599,7 @@ def __call__(self, v):
             return v
         return self.ring().ideal(v)
 
-#############################################################
-# TODO: make those two into real categories (with super_category, ...)
-
-# SimplicialComplex
-#############################################################
-class SimplicialComplexes(Category):
-    """
-    The category of simplicial complexes.
-
-    EXAMPLES::
-
-        sage: SimplicialComplexes()
-        Category of simplicial complexes
-
-    TESTS::
-
-        sage: TestSuite(SimplicialComplexes()).run()
-    """
-
-    def super_categories(self):
-        """
-        EXAMPLES::
-
-            sage: SimplicialComplexes().super_categories()
-            [Category of objects]
-        """
-        return [Objects()] # anything better?
-
+# TODO: make this into a better category
 #############################################################
 # ChainComplex
 #############################################################

src/sage/categories/category_with_axiom.py

@@ -1675,6 +1675,7 @@ class ``Sets.Finite``), or in a separate file (typically in a class
 
 all_axioms = AxiomContainer()
 all_axioms += ("Flying", "Blue",
+              "Compact", "Complex", "Differentiable", "Smooth",
               "Facade", "Finite", "Infinite",
               "FiniteDimensional", "Connected", "WithBasis",
               "Irreducible",

src/sage/categories/cw_complexes.py

@@ -0,0 +1,162 @@
+r"""
+CW Complexes
+"""
+#*****************************************************************************
+#  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.misc.abstract_method import abstract_method
+from sage.misc.cachefunc import cached_method
+from sage.categories.category_singleton import Category_singleton
+from sage.categories.category_with_axiom import CategoryWithAxiom
+from sage.categories.sets_cat import Sets
+
+class CWComplexes(Category_singleton):
+    r"""
+    The category of CW complexes.
+
+    A CW complex is a Closure-finite cell complex in the Weak toplogy.
+
+    REFERENCES:
+
+    - :wikipedia:`CW_complex`
+
+    EXAMPLES::
+
+        sage: from sage.categories.cw_complexes import CWComplexes
+        sage: C = CWComplexes(); C
+        Category of CW complexes
+
+    TESTS::
+
+        sage: TestSuite(C).run()
+    """
+    @cached_method
+    def super_categories(self):
+        """
+        EXAMPLES::
+
+            sage: from sage.categories.cw_complexes import CWComplexes
+            sage: CWComplexes().super_categories()
+            [Category of topological spaces]
+        """
+        return [Sets().Topological()]
+
+    def _repr_object_names(self):
+        """
+        EXAMPLES::
+
+            sage: from sage.categories.cw_complexes import CWComplexes
+            sage: CWComplexes()
+            Category of CW complexes
+        """
+        return "CW complexes"
+
+    class SubcategoryMethods:
+        @cached_method
+        def Connected(self):
+            """
+            Return the full subcategory of the connected objects of ``self``.
+
+            EXAMPLES::
+
+                sage: from sage.categories.cw_complexes import CWComplexes
+                sage: CWComplexes().Connected()
+                Category of connected CW complexes
+
+            TESTS::
+
+                sage: TestSuite(CWComplexes().Connected()).run()
+                sage: CWComplexes().Connected.__module__
+                'sage.categories.cw_complexes'
+            """
+            return self._with_axiom('Connected')
+
+        @cached_method
+        def FiniteDimensional(self):
+            """
+            Return the full subcategory of the finite dimensional
+            objects of ``self``.
+
+            EXAMPLES::
+
+                sage: from sage.categories.cw_complexes import CWComplexes
+                sage: C = CWComplexes().FiniteDimensional(); C
+                Category of finite dimensional CW complexes
+
+            TESTS::
+
+                sage: from sage.categories.cw_complexes import CWComplexes
+                sage: C = CWComplexes().FiniteDimensional()
+                sage: TestSuite(C).run()
+                sage: CWComplexes().Connected().FiniteDimensional.__module__
+                'sage.categories.cw_complexes'
+            """
+            return self._with_axiom('FiniteDimensional')
+
+    class Connected(CategoryWithAxiom):
+        """
+        The category of connected CW complexes.
+        """
+
+    class FiniteDimensional(CategoryWithAxiom):
+        """
+        Category of finite dimensional CW complexes.
+        """
+
+    class Finite(CategoryWithAxiom):
+        """
+        Category of finite CW complexes.
+        """
+        def extra_super_categories(self):
+            """
+            Return the extra super categories of ``self``.
+
+            A finite CW complex is a compact finite-dimensional CW complex.
+            """
+            return [CWComplexes().FiniteDimensional(), Sets().Topological().Compact()]
+
+        class ParentMethods:
+            @cached_method
+            def dimension(self):
+                """
+                Return the dimension of ``self``.
+                """
+                return max(c.dimension() for c in self.cells())
+
+    def Compact_extra_super_categories(self):
+        """
+        Return extraneous super categories for ``CWComplexes().Compact()``.
+
+        A compact CW complex is finite, see Proposition A.1 in [Hat]_.
+
+        .. TODO::
+
+            Fix the name of finite CW complexes.
+
+        EXAMPLES::
+
+            sage: from sage.categories.cw_complexes import CWComplexes
+            sage: CWComplexes().Compact()
+            Category of finite finite dimensional CW complexes
+            sage: CWComplexes().Compact() is CWComplexes().Finite()
+            True
+        """
+        return (Sets().Finite(),)
+
+    class ParentMethods:
+        @abstract_method
+        def dimension(self):
+            """
+            Return the dimension of ``self``.
+            """
+
+        @abstract_method(optional=True)
+        def cells(self):
+            """
+            Return the cells of ``self``.
+            """
+

src/sage/categories/graphs.py

@@ -0,0 +1,61 @@
+"""
+Graphs
+"""
+#*****************************************************************************
+#  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.misc.abstract_method import abstract_method
+from sage.misc.cachefunc import cached_method
+from sage.categories.category_singleton import Category_singleton
+from sage.categories.simplicial_complexes import SimplicialComplexes
+
+class Graphs(Category_singleton):
+    r"""
+    The category of graphs.
+
+    EXAMPLES::
+
+        sage: from sage.categories.graphs import Graphs
+        sage: C = Graphs(); C
+        Category of graphs
+
+    TESTS::
+
+        sage: TestSuite(C).run()
+    """
+    @cached_method
+    def super_categories(self):
+        """
+        EXAMPLES::
+
+            sage: from sage.categories.graphs import Graphs
+            sage: Graphs().super_categories()
+            [Category of simplicial complexes]
+        """
+        return [SimplicialComplexes()]
+
+    class ParentMethods:
+        def dimension(self):
+            """
+            Return the dimension of ``self`` as a CW complex.
+            """
+            if self.edges():
+                return 1
+            return 0
+
+        def facets(self):
+            """
+            Return the facets of ``self``.
+            """
+            return self.edges()
+
+        def faces(self):
+            """
+            Return the faces of ``self``.
+            """
+            return set(self.edges()).union(self.vertices())
+

src/sage/categories/lie_groups.py

@@ -8,68 +8,46 @@
 #                  http://www.gnu.org/licenses/
 #******************************************************************************
 
-from sage.misc.abstract_method import abstract_method
+#from sage.misc.abstract_method import abstract_method
 from sage.misc.cachefunc import cached_method
-from sage.misc.lazy_attribute import lazy_attribute
-from sage.misc.lazy_import import LazyImport
-from sage.categories.category import Category
-from sage.categories.category_types import Category_over_base_ring
-from sage.categories.sets_cat import Sets
+from sage.categories.category_singleton import Category_singleton
 from sage.categories.groups import Groups
 from sage.categories.manifolds import Manifolds
-from sage.rings.all import RR
 
-class LieGroups(Category_over_base_ring):
+class LieGroups(Category_singleton):
     r"""
     The category of Lie groups.
 
-    A Lie group is a topological group with a smooth differentiable
-    manifold structure.
-
-    INPUT:
-
-    - ``k`` -- (default: ``RR``) the field `k`
+    A Lie group is a topological group with a smooth manifold structure.
 
     EXAMPLES::
 
         sage: from sage.categories.lie_groups import LieGroups
         sage: C = LieGroups(); C
-        Category of manifolds over Real Field
-        sage: C.super_categories()
-        [Category of additive commutative additive associative additive unital distributive magmas and additive magmas,
-         Category of modules over Integer Ring]
-        sage: C = LieGroups(CC); C
-        Category of manifolds over Complex Field
+        Category of Lie groups
 
     TESTS::
 
         sage: TestSuite(C).run()
     """
-    def __init__(self, R=RR):
-        """
-        Initialize ``self``.
-        """
-        Category_over_base_ring.__init__(self, RR)
-
     @cached_method
     def super_categories(self):
         """
         EXAMPLES::
 
             sage: from sage.categories.lie_groups import LieGroups
             sage: LieGroups().super_categories()
+            [Category of topological groups, Category of smooth manifolds]
         """
-        R = self.base_ring()
-        # TODO: Make this smooth differentiable manifolds
-        return [Groups().Topological(), Manifolds(R)]
+        return [Groups().Topological(), Manifolds().Smooth()]
 
     def additional_structure(self):
         r"""
         Return ``None``.
 
         Indeed, the category of Lie groups defines no new
         structure: a morphism of topological spaces and of smooth
-        differentiable manifolds is a morphism as Lie groups.
+        manifolds is a morphism as Lie groups.
 
         .. SEEALSO:: :meth:`Category.additional_structure`
 
@@ -80,3 +58,14 @@ def additional_structure(self):
         """
         return None
 
+    # Because Lie is a name that deserves to be capitalized
+    def _repr_object_names(self):
+        """
+        EXAMPLES::
+
+            sage: from sage.categories.lie_groups import LieGroups
+            sage: LieGroups() # indirect doctest
+            Category of Lie groups
+        """
+        return "Lie groups"
+