From 7569a9509a9dbdb3a6dbc603f8bc53d65e2e0480 Mon Sep 17 00:00:00 2001
From: Matthias Koeppe <mkoeppe@math.ucdavis.edu>
Date: Thu, 18 Aug 2022 22:14:03 -0700
Subject: [PATCH] src/sage/categories/finitely_enumerated_families.py: New

---
 .../finitely_enumerated_families.py           | 53 +++++++++++++++++++
 src/sage/sets/family.py                       | 28 +++++-----
 2 files changed, 69 insertions(+), 12 deletions(-)
 create mode 100644 src/sage/categories/finitely_enumerated_families.py

diff --git a/src/sage/categories/finitely_enumerated_families.py b/src/sage/categories/finitely_enumerated_families.py
new file mode 100644
index 00000000000..08ca4cabcbc
--- /dev/null
+++ b/src/sage/categories/finitely_enumerated_families.py
@@ -0,0 +1,53 @@
+r"""
+Finitely 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.finite_enumerated_sets import FiniteEnumeratedSets
+from sage.categories.enumerated_families import EnumeratedFamilies
+
+
+class FinitelyEnumeratedFamilies(Category_singleton):
+    r"""
+    The category of finitely enumerated families
+
+    An *finitely enumerated family* is an enumerated family whose keys
+    form a finite enumerated set; this implies that the family is a finite set.
+
+    EXAMPLES::
+
+        sage: from sage.categories.enumerated_families import EnumeratedFamilies
+        sage: from sage.categories.finitely_enumerated_families import FinitelyEnumeratedFamilies
+        sage: FinitelyEnumeratedFamilies()
+        Category of finitely enumerated families
+
+        sage: FinitelyEnumeratedFamilies() == EnumeratedFamilies() & FiniteSets()
+        False
+        sage: F = Family(ZZ, lambda x: x % 7, is_injective=False, category=FiniteSets())
+        sage: F in EnumeratedFamilies() & FiniteSets()
+        True
+        sage: F in FinitelyEnumeratedFamilies()
+        False
+    """
+
+    def super_categories(self):
+        r"""
+        EXAMPLES::
+
+            sage: from sage.categories.finitely_enumerated_families import FinitelyEnumeratedFamilies
+            sage: FinitelyEnumeratedFamilies().super_categories()
+            [Category of enumerated families, Category of finite enumerated sets]
+        """
+        return [EnumeratedFamilies(), FiniteEnumeratedSets()]
diff --git a/src/sage/sets/family.py b/src/sage/sets/family.py
index 62eaff7ea36..db9668a4308 100644
--- a/src/sage/sets/family.py
+++ b/src/sage/sets/family.py
@@ -19,7 +19,7 @@
 
     sage: P = Partitions(3)
     sage: Family(P, lambda x: x).category()
-    Category of finite enumerated families
+    Category of finitely enumerated families
 """
 
 #*****************************************************************************
@@ -46,6 +46,7 @@
 
 from sage.categories.enumerated_families import EnumeratedFamilies
 from sage.categories.enumerated_sets import EnumeratedSets
+from sage.categories.finitely_enumerated_families import FinitelyEnumeratedFamilies
 from sage.categories.families import Families
 from sage.categories.finite_enumerated_sets import FiniteEnumeratedSets
 from sage.categories.infinite_enumerated_sets import InfiniteEnumeratedSets
@@ -1118,25 +1119,28 @@ def __init__(self, set, function, name=None, category=None, is_injective=None, i
             else:
                 is_injective = True
 
+        if category is None:
+            category = Families()
+        else:
+            category &= Families()
+
+        set_category = Sets()
         if set in FiniteEnumeratedSets():
-            set_category = FiniteEnumeratedSets()
+            set_category &= FiniteEnumeratedSets()
+            category &= FinitelyEnumeratedFamilies()
         elif set in InfiniteEnumeratedSets():
             if is_injective:
-                set_category = InfiniteEnumeratedSets()
+                set_category &= InfiniteEnumeratedSets()
             else:
-                set_category = EnumeratedSets()
+                set_category &= EnumeratedSets()
         elif isinstance(set, (list, tuple, range, CombinatorialClass)):
-            set_category = FiniteEnumeratedSets()
+            set_category &= FiniteEnumeratedSets()
         elif set in EnumeratedSets():
-            set_category = EnumeratedSets()
-        else:
-            set_category = Sets()
+            set_category &= EnumeratedSets()
 
-        if category is None:
-            category = Sets()
-        category = Families() & set_category & category
+        category &= set_category
         if set_category.is_subcategory(EnumeratedSets()):
-            category = EnumeratedFamilies() & category
+            category &= EnumeratedFamilies()
 
         try:
             facade = function.codomain()