From 9b0a68293eb085dfa27cbf80844eb1a387d14c82 Mon Sep 17 00:00:00 2001
From: =?UTF-8?q?Fr=C3=A9d=C3=A9ric=20Chapoton?= <chapoton@unistra.fr>
Date: Fri, 21 Nov 2025 17:54:23 +0100
Subject: [PATCH 1/4] introduce the category of Bounded posets

---
 src/sage/categories/category_with_axiom.py   |  1 +
 src/sage/categories/finite_lattice_posets.py | 22 ++++++++++-
 src/sage/categories/lattice_posets.py        | 32 ++++++++--------
 src/sage/categories/posets.py                | 39 ++++++++++++++++++++
 src/sage/combinat/posets/lattices.py         |  2 +-
 5 files changed, 77 insertions(+), 19 deletions(-)

diff --git a/src/sage/categories/category_with_axiom.py b/src/sage/categories/category_with_axiom.py
index 5a98b9e364b..73288c7a3dc 100644
--- a/src/sage/categories/category_with_axiom.py
+++ b/src/sage/categories/category_with_axiom.py
@@ -1689,6 +1689,7 @@ class ``Sets.Finite``), or in a separate file (typically in a class
                "Commutative", "Cocommutative", "Associative",
                "Inverse", "Unital", "Division", "NoZeroDivisors", "Cellular",
                "AdditiveCommutative", "AdditiveAssociative", "AdditiveInverse", "AdditiveUnital",
+               "Bounded",
                "Extremal", "Trim", "Semidistributive", "CongruenceUniform",
                "Distributive", "Stone",
                "Endset",
diff --git a/src/sage/categories/finite_lattice_posets.py b/src/sage/categories/finite_lattice_posets.py
index 6c3af10965f..9e28da9db0f 100644
--- a/src/sage/categories/finite_lattice_posets.py
+++ b/src/sage/categories/finite_lattice_posets.py
@@ -9,6 +9,8 @@
 # *****************************************************************************
 
 from sage.categories.category_with_axiom import CategoryWithAxiom
+from sage.categories.posets import Posets
+from sage.misc.cachefunc import cached_method
 
 
 class FiniteLatticePosets(CategoryWithAxiom):
@@ -19,9 +21,11 @@ class FiniteLatticePosets(CategoryWithAxiom):
     EXAMPLES::
 
         sage: FiniteLatticePosets()
-        Category of finite lattice posets
+        Category of finite bounded lattice posets
         sage: FiniteLatticePosets().super_categories()
-        [Category of lattice posets, Category of finite posets]
+        [Category of lattice posets,
+         Category of finite posets,
+         Category of bounded posets]
         sage: FiniteLatticePosets().example()
         NotImplemented
 
@@ -37,6 +41,20 @@ class FiniteLatticePosets(CategoryWithAxiom):
         True
         sage: TestSuite(C).run()
     """
+    @cached_method
+    def extra_super_categories(self):
+        r"""
+        Return a list of the (immediate) super categories of
+        ``self``, as per :meth:`Category.super_categories`.
+
+        EXAMPLES::
+
+            sage: FiniteLatticePosets().super_categories()
+            [Category of lattice posets,
+             Category of finite posets,
+             Category of bounded posets]
+        """
+        return [Posets().Bounded()]
 
     class ParentMethods:
 
diff --git a/src/sage/categories/lattice_posets.py b/src/sage/categories/lattice_posets.py
index 172e9f58748..b371db20be0 100644
--- a/src/sage/categories/lattice_posets.py
+++ b/src/sage/categories/lattice_posets.py
@@ -201,10 +201,10 @@ class Extremal(CategoryWithAxiom):
         EXAMPLES::
 
             sage: cat = FiniteLatticePosets().Extremal(); cat
-            Category of finite extremal lattice posets
+            Category of finite bounded extremal lattice posets
 
             sage: cat.super_categories()
-            [Category of finite lattice posets,
+            [Category of finite bounded lattice posets,
              Category of extremal lattice posets]
         """
         class ParentMethods:
@@ -226,9 +226,9 @@ class Trim(CategoryWithAxiom):
         EXAMPLES::
 
             sage: cat = FiniteLatticePosets().Trim(); cat
-            Category of finite trim lattice posets
+            Category of finite bounded trim lattice posets
             sage: cat.super_categories()
-            [Category of finite lattice posets,
+            [Category of finite bounded lattice posets,
              Category of trim lattice posets]
         """
         @cached_method
@@ -241,7 +241,7 @@ def extra_super_categories(self):
             EXAMPLES::
 
                 sage: FiniteLatticePosets().Trim().super_categories()
-                [Category of finite lattice posets,
+                [Category of finite bounded lattice posets,
                  Category of trim lattice posets]
             """
             return [LatticePosets().Extremal()]
@@ -265,10 +265,10 @@ class Semidistributive(CategoryWithAxiom):
         EXAMPLES::
 
             sage: cat = FiniteLatticePosets().Semidistributive(); cat
-            Category of finite semidistributive lattice posets
+            Category of finite bounded semidistributive lattice posets
 
             sage: cat.super_categories()
-            [Category of finite lattice posets,
+            [Category of finite bounded lattice posets,
              Category of semidistributive lattice posets]
         """
         class ParentMethods:
@@ -290,9 +290,9 @@ class CongruenceUniform(CategoryWithAxiom):
         EXAMPLES::
 
             sage: cat = FiniteLatticePosets().CongruenceUniform(); cat
-            Category of finite congruence uniform lattice posets
+            Category of finite bounded congruence uniform lattice posets
             sage: cat.super_categories()
-            [Category of finite lattice posets,
+            [Category of finite bounded lattice posets,
              Category of congruence uniform lattice posets]
         """
         @cached_method
@@ -305,7 +305,7 @@ def extra_super_categories(self):
             EXAMPLES::
 
                 sage: FiniteLatticePosets().CongruenceUniform().super_categories()
-                [Category of finite lattice posets,
+                [Category of finite bounded lattice posets,
                  Category of congruence uniform lattice posets]
             """
             return [LatticePosets().Semidistributive()]
@@ -329,10 +329,10 @@ class Distributive(CategoryWithAxiom):
         EXAMPLES::
 
             sage: cat = FiniteLatticePosets().Distributive(); cat
-            Category of finite distributive lattice posets
+            Category of finite bounded distributive lattice posets
 
             sage: cat.super_categories()
-            [Category of finite lattice posets,
+            [Category of finite bounded lattice posets,
              Category of distributive lattice posets]
         """
         @cached_method
@@ -345,7 +345,7 @@ def extra_super_categories(self):
             EXAMPLES::
 
                 sage: FiniteLatticePosets().Distributive().super_categories()
-                [Category of finite lattice posets,
+                [Category of finite bounded lattice posets,
                  Category of distributive lattice posets]
             """
             return [LatticePosets().Trim(),
@@ -371,10 +371,10 @@ class Stone(CategoryWithAxiom):
         EXAMPLES::
 
             sage: cat = FiniteLatticePosets().Stone(); cat
-            Category of finite stone lattice posets
+            Category of finite bounded stone lattice posets
 
             sage: cat.super_categories()
-            [Category of finite lattice posets,
+            [Category of finite bounded lattice posets,
              Category of stone lattice posets]
         """
         @cached_method
@@ -387,7 +387,7 @@ def extra_super_categories(self):
             EXAMPLES::
 
                 sage: FiniteLatticePosets().Stone().super_categories()
-                [Category of finite lattice posets,
+                [Category of finite bounded lattice posets,
                  Category of stone lattice posets]
             """
             return [LatticePosets().Distributive()]
diff --git a/src/sage/categories/posets.py b/src/sage/categories/posets.py
index 665bedc3bac..8de81685775 100644
--- a/src/sage/categories/posets.py
+++ b/src/sage/categories/posets.py
@@ -12,6 +12,7 @@
 from sage.misc.abstract_method import abstract_method
 from sage.misc.lazy_import import LazyImport
 from sage.categories.category import Category
+from sage.categories.category_with_axiom import CategoryWithAxiom
 from sage.categories.sets_cat import Sets
 
 
@@ -719,3 +720,41 @@ class ElementMethods:
         #         sage: x <= y
         #     """
         #     return self.parent().le(self, other)
+
+    class SubcategoryMethods:
+        def Bounded(self):
+            r"""
+            A bounded poset is a poset with a unique maximal element
+            and a unique minimal element.
+
+            EXAMPLES::
+
+                sage: P = posets.DivisorLattice(24)
+                sage: P in Posets().Bounded()
+                True
+            """
+            return self._with_axiom("Bounded")
+
+    class Bounded(CategoryWithAxiom):
+        """
+        The category of bounded posets.
+
+        EXAMPLES::
+
+            sage: cat = Posets().Bounded(); cat
+            Category of bounded posets
+
+            sage: cat.super_categories()
+            [Category of posets]
+        """
+        class ParentMethods:
+            def is_bounded(self):
+                """
+                Return whether ``self`` is a bounded poset.
+
+                EXAMPLES::
+
+                    sage: posets.TamariLattice(4).is_bounded()
+                    True
+                """
+                return True
diff --git a/src/sage/combinat/posets/lattices.py b/src/sage/combinat/posets/lattices.py
index e06fb09627f..035cc9aff4c 100644
--- a/src/sage/combinat/posets/lattices.py
+++ b/src/sage/combinat/posets/lattices.py
@@ -713,7 +713,7 @@ def LatticePoset(data=None, *args, **options):
 
         sage: L = LatticePoset([[1,2],[3],[3]], facade = True)
         sage: L.category()
-        Category of facade finite enumerated lattice posets
+        Category of facade finite enumerated bounded lattice posets
         sage: parent(L[0])
         Integer Ring
         sage: TestSuite(L).run(skip = ['_test_an_element']) # is_parent_of is not yet implemented

From dcec18ef9ee4f9c6717a0159ead189cf81c5818f Mon Sep 17 00:00:00 2001
From: =?UTF-8?q?Fr=C3=A9d=C3=A9ric=20Chapoton?= <chapoton@unistra.fr>
Date: Fri, 21 Nov 2025 19:27:58 +0100
Subject: [PATCH 2/4] fixing one doctest

---
 src/sage/combinat/alternating_sign_matrix.py | 2 +-
 1 file changed, 1 insertion(+), 1 deletion(-)

diff --git a/src/sage/combinat/alternating_sign_matrix.py b/src/sage/combinat/alternating_sign_matrix.py
index 5df9a34cc68..4083a8ebf77 100644
--- a/src/sage/combinat/alternating_sign_matrix.py
+++ b/src/sage/combinat/alternating_sign_matrix.py
@@ -1048,7 +1048,7 @@ class AlternatingSignMatrices(UniqueRepresentation, Parent):
         sage: L
         Finite lattice containing 7 elements
         sage: L.category()
-        Category of facade finite enumerated lattice posets
+        Category of facade finite enumerated bounded lattice posets
     """
 
     def __init__(self, n):

From dd65dbe6e07ab31f61487fb3526cfa482e9d8144 Mon Sep 17 00:00:00 2001
From: =?UTF-8?q?Fr=C3=A9d=C3=A9ric=20Chapoton?= <chapoton@unistra.fr>
Date: Thu, 27 Nov 2025 14:53:52 +0100
Subject: [PATCH 3/4] some tweaks

---
 src/sage/categories/finite_lattice_posets.py | 7 +++----
 1 file changed, 3 insertions(+), 4 deletions(-)

diff --git a/src/sage/categories/finite_lattice_posets.py b/src/sage/categories/finite_lattice_posets.py
index 9e28da9db0f..4abdb072f40 100644
--- a/src/sage/categories/finite_lattice_posets.py
+++ b/src/sage/categories/finite_lattice_posets.py
@@ -9,7 +9,7 @@
 # *****************************************************************************
 
 from sage.categories.category_with_axiom import CategoryWithAxiom
-from sage.categories.posets import Posets
+from sage.categories.lattice_posets import LatticePosets
 from sage.misc.cachefunc import cached_method
 
 
@@ -44,8 +44,7 @@ class FiniteLatticePosets(CategoryWithAxiom):
     @cached_method
     def extra_super_categories(self):
         r"""
-        Return a list of the (immediate) super categories of
-        ``self``, as per :meth:`Category.super_categories`.
+        Implement the fact that a finite lattice is a bounded poset.
 
         EXAMPLES::
 
@@ -54,7 +53,7 @@ def extra_super_categories(self):
              Category of finite posets,
              Category of bounded posets]
         """
-        return [Posets().Bounded()]
+        return [LatticePosets().Bounded()]
 
     class ParentMethods:
 

From f021fdd616a852c9429265f4797e941fcdd1e36e Mon Sep 17 00:00:00 2001
From: =?UTF-8?q?Fr=C3=A9d=C3=A9ric=20Chapoton?= <chapoton@unistra.fr>
Date: Thu, 27 Nov 2025 15:22:55 +0100
Subject: [PATCH 4/4] enhancement of repr : no "bounded finite lattice"

---
 src/sage/categories/category_with_axiom.py   |  2 +-
 src/sage/categories/finite_lattice_posets.py |  2 +-
 src/sage/categories/lattice_posets.py        | 33 ++++++++++----------
 src/sage/combinat/alternating_sign_matrix.py |  2 +-
 src/sage/combinat/posets/lattices.py         |  2 +-
 5 files changed, 21 insertions(+), 20 deletions(-)

diff --git a/src/sage/categories/category_with_axiom.py b/src/sage/categories/category_with_axiom.py
index 73288c7a3dc..f3d52b00507 100644
--- a/src/sage/categories/category_with_axiom.py
+++ b/src/sage/categories/category_with_axiom.py
@@ -1678,6 +1678,7 @@ class ``Sets.Finite``), or in a separate file (typically in a class
                "Differentiable", "Smooth", "Analytic", "AlmostComplex",
                "FinitelyGeneratedAsMagma",
                "WellGenerated",
+               "Bounded",
                "Facade", "Finite", "Infinite", "Enumerated",
                "Complete",
                "Nilpotent",
@@ -1689,7 +1690,6 @@ class ``Sets.Finite``), or in a separate file (typically in a class
                "Commutative", "Cocommutative", "Associative",
                "Inverse", "Unital", "Division", "NoZeroDivisors", "Cellular",
                "AdditiveCommutative", "AdditiveAssociative", "AdditiveInverse", "AdditiveUnital",
-               "Bounded",
                "Extremal", "Trim", "Semidistributive", "CongruenceUniform",
                "Distributive", "Stone",
                "Endset",
diff --git a/src/sage/categories/finite_lattice_posets.py b/src/sage/categories/finite_lattice_posets.py
index 4abdb072f40..42939236314 100644
--- a/src/sage/categories/finite_lattice_posets.py
+++ b/src/sage/categories/finite_lattice_posets.py
@@ -21,7 +21,7 @@ class FiniteLatticePosets(CategoryWithAxiom):
     EXAMPLES::
 
         sage: FiniteLatticePosets()
-        Category of finite bounded lattice posets
+        Category of finite lattice posets
         sage: FiniteLatticePosets().super_categories()
         [Category of lattice posets,
          Category of finite posets,
diff --git a/src/sage/categories/lattice_posets.py b/src/sage/categories/lattice_posets.py
index b371db20be0..f2d35a03e54 100644
--- a/src/sage/categories/lattice_posets.py
+++ b/src/sage/categories/lattice_posets.py
@@ -90,6 +90,7 @@ def join(self, x, y):
             """
 
     class SubcategoryMethods:
+
         def Stone(self):
             r"""
             A Stone lattice `(L, \vee, \wedge)` is a pseudo-complemented
@@ -201,10 +202,10 @@ class Extremal(CategoryWithAxiom):
         EXAMPLES::
 
             sage: cat = FiniteLatticePosets().Extremal(); cat
-            Category of finite bounded extremal lattice posets
+            Category of finite extremal lattice posets
 
             sage: cat.super_categories()
-            [Category of finite bounded lattice posets,
+            [Category of finite lattice posets,
              Category of extremal lattice posets]
         """
         class ParentMethods:
@@ -226,9 +227,9 @@ class Trim(CategoryWithAxiom):
         EXAMPLES::
 
             sage: cat = FiniteLatticePosets().Trim(); cat
-            Category of finite bounded trim lattice posets
+            Category of finite trim lattice posets
             sage: cat.super_categories()
-            [Category of finite bounded lattice posets,
+            [Category of finite lattice posets,
              Category of trim lattice posets]
         """
         @cached_method
@@ -241,7 +242,7 @@ def extra_super_categories(self):
             EXAMPLES::
 
                 sage: FiniteLatticePosets().Trim().super_categories()
-                [Category of finite bounded lattice posets,
+                [Category of finite lattice posets,
                  Category of trim lattice posets]
             """
             return [LatticePosets().Extremal()]
@@ -265,10 +266,10 @@ class Semidistributive(CategoryWithAxiom):
         EXAMPLES::
 
             sage: cat = FiniteLatticePosets().Semidistributive(); cat
-            Category of finite bounded semidistributive lattice posets
+            Category of finite semidistributive lattice posets
 
             sage: cat.super_categories()
-            [Category of finite bounded lattice posets,
+            [Category of finite lattice posets,
              Category of semidistributive lattice posets]
         """
         class ParentMethods:
@@ -290,9 +291,9 @@ class CongruenceUniform(CategoryWithAxiom):
         EXAMPLES::
 
             sage: cat = FiniteLatticePosets().CongruenceUniform(); cat
-            Category of finite bounded congruence uniform lattice posets
+            Category of finite congruence uniform lattice posets
             sage: cat.super_categories()
-            [Category of finite bounded lattice posets,
+            [Category of finite lattice posets,
              Category of congruence uniform lattice posets]
         """
         @cached_method
@@ -305,7 +306,7 @@ def extra_super_categories(self):
             EXAMPLES::
 
                 sage: FiniteLatticePosets().CongruenceUniform().super_categories()
-                [Category of finite bounded lattice posets,
+                [Category of finite lattice posets,
                  Category of congruence uniform lattice posets]
             """
             return [LatticePosets().Semidistributive()]
@@ -329,10 +330,10 @@ class Distributive(CategoryWithAxiom):
         EXAMPLES::
 
             sage: cat = FiniteLatticePosets().Distributive(); cat
-            Category of finite bounded distributive lattice posets
+            Category of finite distributive lattice posets
 
             sage: cat.super_categories()
-            [Category of finite bounded lattice posets,
+            [Category of finite lattice posets,
              Category of distributive lattice posets]
         """
         @cached_method
@@ -345,7 +346,7 @@ def extra_super_categories(self):
             EXAMPLES::
 
                 sage: FiniteLatticePosets().Distributive().super_categories()
-                [Category of finite bounded lattice posets,
+                [Category of finite lattice posets,
                  Category of distributive lattice posets]
             """
             return [LatticePosets().Trim(),
@@ -371,10 +372,10 @@ class Stone(CategoryWithAxiom):
         EXAMPLES::
 
             sage: cat = FiniteLatticePosets().Stone(); cat
-            Category of finite bounded stone lattice posets
+            Category of finite stone lattice posets
 
             sage: cat.super_categories()
-            [Category of finite bounded lattice posets,
+            [Category of finite lattice posets,
              Category of stone lattice posets]
         """
         @cached_method
@@ -387,7 +388,7 @@ def extra_super_categories(self):
             EXAMPLES::
 
                 sage: FiniteLatticePosets().Stone().super_categories()
-                [Category of finite bounded lattice posets,
+                [Category of finite lattice posets,
                  Category of stone lattice posets]
             """
             return [LatticePosets().Distributive()]
diff --git a/src/sage/combinat/alternating_sign_matrix.py b/src/sage/combinat/alternating_sign_matrix.py
index 4083a8ebf77..5df9a34cc68 100644
--- a/src/sage/combinat/alternating_sign_matrix.py
+++ b/src/sage/combinat/alternating_sign_matrix.py
@@ -1048,7 +1048,7 @@ class AlternatingSignMatrices(UniqueRepresentation, Parent):
         sage: L
         Finite lattice containing 7 elements
         sage: L.category()
-        Category of facade finite enumerated bounded lattice posets
+        Category of facade finite enumerated lattice posets
     """
 
     def __init__(self, n):
diff --git a/src/sage/combinat/posets/lattices.py b/src/sage/combinat/posets/lattices.py
index 035cc9aff4c..e06fb09627f 100644
--- a/src/sage/combinat/posets/lattices.py
+++ b/src/sage/combinat/posets/lattices.py
@@ -713,7 +713,7 @@ def LatticePoset(data=None, *args, **options):
 
         sage: L = LatticePoset([[1,2],[3],[3]], facade = True)
         sage: L.category()
-        Category of facade finite enumerated bounded lattice posets
+        Category of facade finite enumerated lattice posets
         sage: parent(L[0])
         Integer Ring
         sage: TestSuite(L).run(skip = ['_test_an_element']) # is_parent_of is not yet implemented