Merge branch 'public/categories/topological_metric_spaces-18175' of t…

…rac.sagemath.org:sage into public/categories/topological_metric_spaces-18175

Conflicts:
	src/sage/categories/groups.py

src/sage/categories/all.py

@@ -2,10 +2,11 @@
 
 from category_types import(
                         Elements,
-                        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

@@ -513,34 +513,7 @@ 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

@@ -1673,6 +1673,7 @@ class ``Sets.Finite``), or in a separate file (typically in a class
 
 all_axioms = AxiomContainer()
 all_axioms += ("Flying", "Blue",
+               "Compact", "Complex", "Differentiable", "Smooth",
                "FinitelyGeneratedAsMagma",
                "Facade", "Finite", "Infinite",
                "FiniteDimensional", "Connected", "WithBasis",

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/groups.py

@@ -19,6 +19,7 @@
 from sage.categories.algebra_functor import AlgebrasCategory
 from sage.categories.cartesian_product import CartesianProductsCategory, cartesian_product
 from sage.categories.finite_enumerated_sets import FiniteEnumeratedSets
+from sage.categories.topological_spaces import TopologicalSpacesCategory
 
 class Groups(CategoryWithAxiom):
     """
@@ -480,6 +481,7 @@ def conjugacy_class(self):
             return self.parent().conjugacy_class(self)
 
     Finite = LazyImport('sage.categories.finite_groups', 'FiniteGroups')
+    Lie = LazyImport('sage.categories.lie_groups', 'LieGroups', 'Lie')
     #Algebras = LazyImport('sage.categories.group_algebras', 'GroupAlgebras')
 
     class Commutative(CategoryWithAxiom):
@@ -942,3 +944,15 @@ def order(self):
                 """
                 from sage.misc.misc_c import prod
                 return prod(c.cardinality() for c in self.cartesian_factors())
+
+    class Topological(TopologicalSpacesCategory):
+        """
+        Category of topological groups.
+
+        A topological group `G` is a group which has a topology such that
+        multiplication and taking inverses are continuous functions.
+
+        REFERENCES:
+
+        - :wikipedia:`Topological_group`
+        """

src/sage/categories/lie_groups.py

@@ -0,0 +1,71 @@
+r"""
+Lie Groups
+"""
+#*****************************************************************************
+#  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.groups import Groups
+from sage.categories.manifolds import Manifolds
+
+class LieGroups(Category_singleton):
+    r"""
+    The category of Lie groups.
+
+    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 Lie groups
+
+    TESTS::
+
+        sage: TestSuite(C).run()
+    """
+    @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]
+        """
+        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
+        manifolds is a morphism as Lie groups.
+
+        .. SEEALSO:: :meth:`Category.additional_structure`
+
+        EXAMPLES::
+
+            sage: from sage.categories.lie_groups import LieGroups
+            sage: LieGroups().additional_structure()
+        """
+        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"
+