16340: reverted change to CoxeterGroups.is_structure_category() + explanations in the doc

Author: nthiery

src/sage/categories/coxeter_groups.py

@@ -32,7 +32,7 @@ class CoxeterGroups(Category_singleton):
 
     `I` is the *index set* of `W` and `|I|` is the *rank* of `W`.
 
-    See http://en.wikipedia.org/wiki/Coxeter_group for details.
+    See :Wikipedia:`Coxeter_group` for details.
 
     EXAMPLES::
 
@@ -67,6 +67,19 @@ class CoxeterGroups(Category_singleton):
 
     .. SEEALSO:: :class:`WeylGroups`, :mod:`sage.combinat.root_system`
 
+    .. WARNING::
+
+        It is assumed that morphisms in this category preserve the
+        distinguished choice of simple reflections. In particular,
+        subobjects in this category are parabolic subgroups. In this
+        sense, this category might be better named ``Coxeter
+        Systems``. In the long run we might want to have two distinct
+        categories, one for Coxeter groups (with morphisms being just
+        group morphisms) and one for Coxeter systems::
+
+            sage: CoxeterGroups().is_full_subcategory(Groups())
+            False
+
     TESTS::
 
         sage: W = CoxeterGroups().example(); TestSuite(W).run(verbose = "True")
@@ -111,23 +124,6 @@ def super_categories(self):
     Finite = LazyImport('sage.categories.finite_coxeter_groups', 'FiniteCoxeterGroups')
     Algebras = LazyImport('sage.categories.coxeter_group_algebras', 'CoxeterGroupAlgebras')
 
-    def is_structure_category(self):
-        r"""
-        Return whether ``self`` is a structure category.
-
-        .. SEEALSO:: :meth:`Category.is_structure_category`
-
-        The category of Coxeter groups defines no new structure:
-        Coxeter groups are a special class of groups.
-
-        EXAMPLES::
-
-            sage: CoxeterGroups().is_structure_category()
-            False
-        """
-        return False
-
-
     class ParentMethods:
 
         @abstract_method