diff --git a/src/sage/algebras/algebra.py b/src/sage/algebras/algebra.py
deleted file mode 100644
index 8d9395a3176..00000000000
--- a/src/sage/algebras/algebra.py
+++ /dev/null
@@ -1,40 +0,0 @@
-# sage.doctest: needs sage.combinat sage.modules
-"""
-Abstract base class for algebras
-"""
-
-#*****************************************************************************
-#       Copyright (C) 2005 William Stein <wstein@gmail.com>
-#
-#  Distributed under the terms of the GNU General Public License (GPL)
-#
-#    This code is distributed in the hope that it will be useful,
-#    but WITHOUT ANY WARRANTY; without even the implied warranty of
-#    MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the GNU
-#    General Public License for more details.
-#
-#  The full text of the GPL is available at:
-#
-#                  http://www.gnu.org/licenses/
-#*****************************************************************************
-
-from sage.categories.algebras import Algebras
-
-
-def is_Algebra(x):
-    r"""
-    Return ``True`` if `x` is an Algebra.
-
-    EXAMPLES::
-
-        sage: from sage.algebras.algebra import is_Algebra
-        sage: R.<x,y> = FreeAlgebra(QQ,2)
-        sage: is_Algebra(R)
-        doctest:warning...
-        DeprecationWarning: the function is_Algebra is deprecated; use '... in Algebras(base_ring)' instead
-        See https://github.com/sagemath/sage/issues/35253 for details.
-        True
-    """
-    from sage.misc.superseded import deprecation
-    deprecation(35253, "the function is_Algebra is deprecated; use '... in Algebras(base_ring)' instead")
-    return x in Algebras(x.base_ring())
diff --git a/src/sage/algebras/meson.build b/src/sage/algebras/meson.build
index d3483851743..bad93c41abf 100644
--- a/src/sage/algebras/meson.build
+++ b/src/sage/algebras/meson.build
@@ -1,7 +1,6 @@
 py.install_sources(
   '__init__.py',
   'affine_nil_temperley_lieb.py',
-  'algebra.py',
   'all.py',
   'askey_wilson.py',
   'associated_graded.py',
diff --git a/src/sage/categories/modules.py b/src/sage/categories/modules.py
index f9bc036910f..0f7ec03001a 100644
--- a/src/sage/categories/modules.py
+++ b/src/sage/categories/modules.py
@@ -967,16 +967,10 @@ def construction(self):
                      (Free Algebra on 2 generators (None0, None1) over Rational Field,
                       Free Algebra on 2 generators (None0, None1) over Rational Field))
                 """
-                try:
-                    factors = self.tensor_factors()
-                except (TypeError, NotImplementedError):
-                    from sage.misc.superseded import deprecation
-                    deprecation(34393, "implementations of Modules().TensorProducts() now must define the method tensor_factors")
-                    return None
-                return (TensorProductFunctor(),
-                        factors)
-
-            @abstract_method(optional=True)
+                factors = self.tensor_factors()
+                return (TensorProductFunctor(), factors)
+
+            @abstract_method
             def tensor_factors(self):
                 """
                 Return the tensor factors of this tensor product.
@@ -992,16 +986,4 @@ def tensor_factors(self):
                     F # G
                     sage: T.tensor_factors()
                     (F, G)
-
-                TESTS::
-
-                    sage: Cat = ModulesWithBasis(ZZ).FiniteDimensional().TensorProducts()
-                    sage: M = CombinatorialFreeModule(ZZ,                               # needs sage.modules
-                    ....:                             ((1, 1), (1, 2), (2, 1), (2, 2)),
-                    ....:                             category=Cat)
-                    sage: M.construction()                                              # needs sage.modules
-                    doctest:warning...
-                    DeprecationWarning: implementations of Modules().TensorProducts() now must define the method tensor_factors
-                    See https://github.com/sagemath/sage/issues/34393 for details.
-                    (VectorFunctor, Integer Ring)
                 """