Merge branch '26161' into 26103

Author: saraedum

src/sage/rings/polynomial/polynomial_quotient_ring.py

@@ -387,6 +387,18 @@ def __init__(self, ring, polynomial, name=None, category=None):
             sage: S == PolynomialQuotientRing_generic(R,x^2-4,'xbar')
             True
 
+        Check that :trac:`26161` has been resolved::
+
+            sage: R.<x> = GF(2)[]
+            sage: S = R.quo(x)
+            sage: S in FiniteFields()
+            True
+            sage: type(S).mro()
+            [<class 'sage.rings.polynomial.polynomial_quotient_ring.PolynomialQuotientRing_field_with_category'>,
+            ...
+             <class 'sage.categories.finite_fields.FiniteFields.parent_class'>,
+            ...
+
         """
         if not isinstance(ring, PolynomialRing_commutative):
             raise TypeError("R must be a univariate polynomial ring.")
@@ -401,6 +413,9 @@ def __init__(self, ring, polynomial, name=None, category=None):
         self.__polynomial = polynomial
         category = CommutativeAlgebras(ring.base_ring()).Quotients().or_subcategory(category)
         if self.is_finite():
+            # We refine the category for finite quotients.
+            # Note that is_finite() is cheap so it does not seem to do a lazy
+            # _refine_category_() in is_finite() as we do for is_field()
             category = category.Finite()
         CommutativeRing.__init__(self, ring, names=name, category=category)