From 1eff5e5c988bab27748bbd57112d0f4b76361e37 Mon Sep 17 00:00:00 2001
From: user202729 <25191436+user202729@users.noreply.github.com>
Date: Thu, 28 Nov 2024 15:12:29 +0700
Subject: [PATCH 1/2] Fix construct homset of elliptic curve in Sets()

---
 src/sage/schemes/elliptic_curves/ell_field.py | 21 ++++++++++++++-----
 src/sage/schemes/generic/homset.py            | 19 ++++++++++++++++-
 2 files changed, 34 insertions(+), 6 deletions(-)

diff --git a/src/sage/schemes/elliptic_curves/ell_field.py b/src/sage/schemes/elliptic_curves/ell_field.py
index 4f694e0f252..f5d4d396291 100755
--- a/src/sage/schemes/elliptic_curves/ell_field.py
+++ b/src/sage/schemes/elliptic_curves/ell_field.py
@@ -1150,12 +1150,23 @@ def _Hom_(self, other, category=None):
             sage: E = EllipticCurve(GF(19), [1,0])
             sage: type(E._Hom_(E))
             <class 'sage.schemes.elliptic_curves.homset.EllipticCurveHomset_with_category'>
+
+        TESTS::
+
+            sage: E.Hom(E, Sets())
+            Set of Morphisms from Elliptic Curve defined by y^2 = x^3 + x over Finite Field of size 19 to Elliptic Curve defined by y^2 = x^3 + x over Finite Field of size 19 in Category of sets
+            sage: E.Hom(E, Sets())(lambda x: x + E(3, 7))(E(4, 7))
+            (12 : 12 : 1)
         """
-        if isinstance(other, ell_generic.EllipticCurve_generic) and self.base_ring() == other.base_ring():
-            from . import homset
-            return homset.EllipticCurveHomset(self, other, category=category)
-        from sage.schemes.generic.homset import SchemeHomset_generic
-        return SchemeHomset_generic(self, other, category=category)
+        from sage.categories.schemes import Schemes
+        if category is None or category.is_subcategory(Schemes()):
+            if isinstance(other, ell_generic.EllipticCurve_generic) and self.base_ring() == other.base_ring():
+                from . import homset
+                return homset.EllipticCurveHomset(self, other, category=category)
+            from sage.schemes.generic.homset import SchemeHomset_generic
+            return SchemeHomset_generic(self, other, category=category)
+        from sage.categories.homset import Homset
+        return Homset(self, other, category=category)
 
     def isogeny(self, kernel, codomain=None, degree=None, model=None, check=True, algorithm=None, velu_sqrt_bound=None):
         r"""
diff --git a/src/sage/schemes/generic/homset.py b/src/sage/schemes/generic/homset.py
index 370049d2238..bc0995470e1 100755
--- a/src/sage/schemes/generic/homset.py
+++ b/src/sage/schemes/generic/homset.py
@@ -249,15 +249,32 @@ class SchemeHomset_generic(HomsetWithBase):
 
         sage: from sage.schemes.generic.homset import SchemeHomset_generic
         sage: A2 = AffineSpace(QQ,2)
-        sage: Hom = SchemeHomset_generic(A2, A2); Hom
+        sage: Hom = A2.Hom(A2); Hom
         Set of morphisms
           From: Affine Space of dimension 2 over Rational Field
           To:   Affine Space of dimension 2 over Rational Field
         sage: Hom.category()
         Category of endsets of schemes over Rational Field
+
+    TESTS::
+
+        sage: Hom = SchemeHomset_generic(A2, A2); Hom
+        Set of morphisms
+          From: Affine Space of dimension 2 over Rational Field
+          To:   Affine Space of dimension 2 over Rational Field
+        sage: Hom = SchemeHomset_generic(A2, A2, Sets())
+        Traceback (most recent call last):
+        ...
+        ValueError: Cannot create SchemeHomset with category = Category of sets. Consider using Homset instead
     """
     Element = SchemeMorphism
 
+    def __init__(self, X, Y, category=None, check=True, base=None):
+        super().__init__(X, Y, category, check, base)
+        from sage.categories.schemes import Schemes
+        if check and category is not None and not category.is_subcategory(Schemes()):
+            raise ValueError(f"Cannot create SchemeHomset with category = {category}. Consider using Homset instead")
+
     def __reduce__(self):
         """
         Used in pickling.

From 60ad5f20ea391e2010e67b9743a50ba3f3a9e03d Mon Sep 17 00:00:00 2001
From: user202729 <25191436+user202729@users.noreply.github.com>
Date: Thu, 28 Nov 2024 21:03:20 +0700
Subject: [PATCH 2/2] Fix category of GluedScheme

---
 src/sage/schemes/generic/glue.py | 14 ++++++++++++++
 1 file changed, 14 insertions(+)

diff --git a/src/sage/schemes/generic/glue.py b/src/sage/schemes/generic/glue.py
index 7733030a2ab..a13aec6b982 100755
--- a/src/sage/schemes/generic/glue.py
+++ b/src/sage/schemes/generic/glue.py
@@ -44,6 +44,14 @@ class GluedScheme(Scheme):
           X: Spectrum of Univariate Polynomial Ring in x over Rational Field
           Y: Spectrum of Univariate Polynomial Ring in y over Rational Field
           U: Spectrum of Quotient of Multivariate Polynomial Ring in x, y over Rational Field by the ideal (x*y - 1)
+
+    TESTS::
+
+        sage: S = Sx.glue_along_domains(Sy)
+        sage: S.base_ring()
+        Integer Ring
+        sage: S.category()
+        Category of schemes
     """
     def __init__(self, f, g, check=True):
         if check:
@@ -55,6 +63,12 @@ def __init__(self, f, g, check=True):
                 raise ValueError("f (=%s) and g (=%s) must have the same domain" % (f,g))
         self.__f = f
         self.__g = g
+        category = f.codomain().category()._meet_(g.codomain().category())
+        from sage.structure.element import get_coercion_model
+        base_ring = get_coercion_model().common_parent(
+                f.codomain().base_ring(), g.codomain().base_ring())
+        Scheme.__init__(self, None, category)
+        self._base_ring = base_ring
 
     def gluing_maps(self):
         r"""