16340: revert change, and add documentation thereabout: the category of permutation groups defines additional structure

Author: nthiery

src/sage/categories/permutation_groups.py

@@ -18,7 +18,12 @@ class PermutationGroups(Category):
     The category of permutation groups.
 
     A *permutation group* is a group whose elements are concretely
-    represented by permutations of some set.
+    represented by permutations of some set. In other words, the group
+    comes endowed with a distinguished action on some set.
+
+    This distinguished action should be preserved by permutation group
+    morphisms. For details, see
+    :Wikipedia:`Permutation_group#Permutation_isomorphic_groups`.
 
     .. TODO:: shall we accept only permutations with finite support or not?
 
@@ -29,6 +34,13 @@ class PermutationGroups(Category):
         sage: PermutationGroups().super_categories()
         [Category of groups]
 
+    The category of permutation groups defines additional structure
+    that should be preserved by morphisms, namely the distinguished
+    action::
+
+        sage: PermutationGroups().is_structure_category()
+        True
+
     TESTS::
 
         sage: C = PermutationGroups()
@@ -46,20 +58,4 @@ def super_categories(self):
         """
         return [Groups()]
 
-    def is_structure_category(self):
-        r"""
-        Return whether ``self`` is a structure category.
-
-        .. SEEALSO:: :meth:`Category.is_structure_category`
-
-        The category of permutations groups defines no new structure:
-        permutation groups are a special class of groups.
-
-        EXAMPLES::
-
-            sage: PermutationGroups().is_structure_category()
-            False
-        """
-        return False
-
     Finite = LazyImport('sage.categories.finite_permutation_groups', 'FinitePermutationGroups')