gh-36897: some ruff fixes (UP034 and UP039 codes) and error links in categories
    
Adding a few links on errors in the doc

Also fixing a few ruff UP details

### 📝 Checklist

- [x] The title is concise, informative, and self-explanatory.
- [x] The description explains in detail what this PR is about.
    
URL: #36897
Reported by: Frédéric Chapoton
Reviewer(s): David Coudert

Author: Release Manager

src/sage/categories/algebras_with_basis.py

@@ -1,13 +1,13 @@
 r"""
 Algebras With Basis
 """
-#*****************************************************************************
+# ****************************************************************************
 #  Copyright (C) 2008      Teresa Gomez-Diaz (CNRS) <[email protected]>
 #                2008-2013 Nicolas M. Thiery <nthiery at users.sf.net>
 #
 #  Distributed under the terms of the GNU General Public License (GPL)
 #                  https://www.gnu.org/licenses/
-#******************************************************************************
+# *****************************************************************************
 
 from sage.categories.cartesian_product import CartesianProductsCategory
 from sage.categories.category_with_axiom import CategoryWithAxiom_over_base_ring
@@ -106,7 +106,7 @@ class AlgebrasWithBasis(CategoryWithAxiom_over_base_ring):
         sage: TestSuite(AlgebrasWithBasis(QQ)).run()
     """
 
-    def example(self, alphabet=('a','b','c')):
+    def example(self, alphabet=('a', 'b', 'c')):
         """
         Return an example of algebra with basis.
 
@@ -259,7 +259,7 @@ def one_from_cartesian_product_of_one_basis(self):
                     ....:                    SymmetricGroupAlgebra(QQ, 4)]).one()
                     B[(0, [1, 2, 3])] + B[(1, [1, 2, 3, 4])]
                 """
-                return self.sum_of_monomials( zip( self._sets_keys(), (set.one_basis() for set in self._sets)) )
+                return self.sum_of_monomials(zip(self._sets_keys(), (set.one_basis() for set in self._sets)))
 
             @lazy_attribute
             def one(self):
@@ -370,7 +370,8 @@ def product_on_basis(self, t1, t2):
 
                 TODO: optimize this implementation!
                 """
-                return tensor( (module.monomial(x1)*module.monomial(x2) for (module, x1, x2) in zip(self._sets, t1, t2)) ) #.
+                return tensor(module.monomial(x1) * module.monomial(x2)
+                              for module, x1, x2 in zip(self._sets, t1, t2))
 
         class ElementMethods:
             """

src/sage/categories/category.py

@@ -565,7 +565,7 @@ def an_instance(cls):
     def __call__(self, x, *args, **opts):
         """
         Construct an object in this category from the data in ``x``,
-        or throw ``TypeError`` or ``NotImplementedError``.
+        or throw :class:`TypeError` or :class:`NotImplementedError`.
 
         If ``x`` is readily in ``self`` it is returned unchanged.
         Categories wishing to extend this minimal behavior should
@@ -583,7 +583,7 @@ def __call__(self, x, *args, **opts):
     def _call_(self, x):
         """
         Construct an object in this category from the data in ``x``,
-        or throw ``NotImplementedError``.
+        or throw :class:`NotImplementedError`.
 
         EXAMPLES::
 

src/sage/categories/coxeter_groups.py

@@ -701,7 +701,7 @@ def _test_reduced_word(self, **options):
             for x in tester.some_elements():
                 red = x.reduced_word()
                 tester.assertEqual(self.from_reduced_word(red), x)
-                tester.assertEqual(self.prod((s[i] for i in red)), x)
+                tester.assertEqual(self.prod(s[i] for i in red), x)
 
         def simple_projection(self, i, side='right', length_increasing=True):
             r"""

src/sage/categories/crystals.py

@@ -578,7 +578,7 @@ def _Hom_(self, Y, category=None, **options):
             The sole purpose of this method is to construct the homset
             as a :class:`~sage.categories.crystals.CrystalHomset`. If
             ``category`` is specified and is not a subcategory of
-            :class:`Crystals`, a ``TypeError`` is raised instead.
+            :class:`Crystals`, a :class:`TypeError` is raised instead.
 
             This method is not meant to be called directly. Please use
             :func:`sage.categories.homset.Hom` instead.

src/sage/categories/enumerated_sets.py

@@ -182,7 +182,8 @@ def __iter__(self):
             It is also possible to override ``__iter__`` method itself. Then
             the methods of the first column are defined using  ``__iter__``
 
-            If none of these are provided, raise a ``NotImplementedError``.
+            If none of these are provided, this raises
+            a :class:`NotImplementedError`.
 
             EXAMPLES:
 
@@ -928,7 +929,7 @@ def random_element(self):
             the probability is uniform.
 
             This is a generic implementation from the category
-            ``EnumeratedSets()``. It raise a ``NotImplementedError``
+            ``EnumeratedSets()``. It raises a :class:`NotImplementedError`
             since one does not know whether the set is finite.
 
             EXAMPLES::

src/sage/categories/facade_sets.py

@@ -209,8 +209,8 @@ def _an_element_(self):
 
             For each parent ``self`` is a facade for, this default
             implementation tries the method ``an_element`` until it finds an
-            element in ``self``. If none is found raise a
-            ``NotImplementedError``.
+            element in ``self``. If none is found, this raises a
+            :class:`NotImplementedError`.
 
             EXAMPLES::
 

src/sage/categories/fields.py

@@ -808,7 +808,7 @@ def inverse_of_unit(self):
                 1/2
 
             Trying to invert the zero element typically raises a
-            ``ZeroDivisionError``::
+            :class:`ZeroDivisionError`::
 
                 sage: QQ(0).inverse_of_unit()
                 Traceback (most recent call last):

src/sage/categories/filtered_modules_with_basis.py

@@ -156,7 +156,7 @@ def basis(self, d=None):
                  over Integer Ring(i))_{i in Partitions}
 
             Checking this method on a filtered algebra. Note that this
-            will typically raise a ``NotImplementedError`` when this
+            will typically raise a :class:`NotImplementedError` when this
             feature is not implemented. ::
 
                 sage: A = AlgebrasWithBasis(ZZ).Filtered().example()

src/sage/categories/finite_groups.py

@@ -153,9 +153,9 @@ def conjugacy_classes(self):
             Return a list with all the conjugacy classes of the group.
 
             This will eventually be a fall-back method for groups not defined
-            over GAP. Right now just raises a ``NotImplementedError``, until
-            we include a non-GAP way of listing the conjugacy classes
-            representatives.
+            over GAP. Right now, it just raises a
+            :class:`NotImplementedError`, until we include a non-GAP
+            way of listing the conjugacy classes representatives.
 
             EXAMPLES::
 

src/sage/categories/finite_posets.py

@@ -906,7 +906,7 @@ def birational_toggle(self, v, labelling):
             encoded to be understood by Sage. This implementation allows
             `\mathbf{K}` to be a semifield, not just a field. The birational
             `v`-toggle is only a rational map, so an exception (most
-            likely, ``ZeroDivisionError``) will be thrown if the
+            likely, :class:`ZeroDivisionError`) will be thrown if the
             denominator is zero.
 
             INPUT:
@@ -1121,7 +1121,7 @@ def birational_toggles(self, vs, labelling):
             encoded to be understood by Sage. This implementation allows
             `\mathbf{K}` to be a semifield, not just a field. The birational
             `v`-toggle is only a rational map, so an exception (most
-            likely, ``ZeroDivisionError``) will be thrown if the
+            likely, :class:`ZeroDivisionError`) will be thrown if the
             denominator is zero.
 
             INPUT:
@@ -1194,9 +1194,10 @@ def birational_rowmotion(self, labelling):
             `\mathbf{K}`-labellings and for an explanation of how
             `\mathbf{K}`-labellings are to be encoded to be understood
             by Sage. This implementation allows `\mathbf{K}` to be a
-            semifield, not just a field. Birational rowmotion is only a
-            rational map, so an exception (most likely, ``ZeroDivisionError``)
-            will be thrown if the denominator is zero.
+            semifield, not just a field. Birational rowmotion is only
+            a rational map, so an exception (most likely,
+            :class:`ZeroDivisionError`) will be thrown if the
+            denominator is zero.
 
             INPUT: