src/sage/categories/enumerated_families.py: New

src/sage/categories/enumerated_families.py

@@ -0,0 +1,63 @@
+r"""
+Enumerated families
+"""
+
+#*****************************************************************************
+#       Copyright (C) 2022 Matthias Koeppe
+#
+# This program is free software: you can redistribute it and/or modify
+# it under the terms of the GNU General Public License as published by
+# the Free Software Foundation, either version 2 of the License, or
+# (at your option) any later version.
+#                  https://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.enumerated_sets import EnumeratedSets
+from sage.categories.families import Families
+
+
+class EnumeratedFamilies(Category_singleton):
+    r"""
+    The category of enumerated families
+
+    An *enumerated family* is a family whose keys are an enumerated set
+    that induces an enumeration of the family.
+
+    - ``F[key]``: the value (element) indexed by ``key``.
+
+    The standard methods for a family ``F`` are:
+
+    - ``F.keys()``, ``F.values()``, ``F.items()``: methods similar to those of
+      :class:`dict` (or :class:`collections.abc.Mapping`).
+
+    The map is not necessarily injective.
+
+    - ``iter(F)``: returns an iterator for the elements (values) of ``F`` as a set
+      in the same order as ``iter(F.values())``, but with duplicates removed.
+
+    EXAMPLES::
+
+        sage: from sage.categories.enumerated_families import EnumeratedFamilies
+        sage: from sage.categories.families import Families
+        sage: EnumeratedFamilies()
+        Category of enumerated families
+
+        sage: EnumeratedFamilies() == Families() & EnumeratedSets()
+        False
+
+        sage: Families() & EnumeratedSets()  # BUG
+        Category of enumerated families
+    """
+
+    def super_categories(self):
+        r"""
+        EXAMPLES::
+
+            sage: from sage.categories.enumerated_families import EnumeratedFamilies
+            sage: EnumeratedFamilies().super_categories()
+            [Category of families, Category of enumerated sets]
+        """
+        return [Families(), EnumeratedSets()]

src/sage/categories/families.py

@@ -14,6 +14,8 @@
 
 from sage.misc.abstract_method import abstract_method
 from sage.misc.cachefunc import cached_method
+from sage.misc.lazy_import import LazyImport
+from sage.categories.category_with_axiom import CategoryWithAxiom
 from sage.categories.category_singleton import Category_singleton
 from sage.categories.sets_cat import Sets
 
@@ -65,24 +67,6 @@ def super_categories(self):
         """
         return [Sets()]
 
-    ## def additional_structure(self):
-    ##     r"""
-    ##     Return ``self``.
-
-    ##     Indeed, the category of families defines an
-    ##     additional structure, namely the map from keys onto it,
-    ##     which shall be preserved by morphisms.
-
-    ##     .. SEEALSO:: :meth:`Category.additional_structure`
-
-    ##     EXAMPLES::
-
-    ##         sage: from sage.categories.families import Families
-    ##         sage: Families().additional_structure()
-    ##         Category of families
-    ##     """
-    ##     return self
-
     class ParentMethods:
 
         #def __getitem__(self, i):