diff --git a/src/sage/categories/category_singleton.pyx b/src/sage/categories/category_singleton.pyx
index d907eedb9e8..6cd17581630 100644
--- a/src/sage/categories/category_singleton.pyx
+++ b/src/sage/categories/category_singleton.pyx
@@ -218,9 +218,9 @@ class Category_singleton(Category):
              <class 'sage.categories.category_singleton.Category_singleton'>,
              <class 'sage.categories.category.Category'>,
              <class 'sage.structure.unique_representation.UniqueRepresentation'>,
+             <class 'sage.misc.fast_methods.WithEqualityById'>,
              <class 'sage.structure.unique_representation.CachedRepresentation'>,
              <class 'sage.structure.unique_representation.WithPicklingByInitArgs'>,
-             <class 'sage.misc.fast_methods.WithEqualityById'>,
              <class 'sage.structure.sage_object.SageObject'>,
              <class '__main__.R.subcategory_class'>,
              <class 'sage.categories.sets_cat.Sets.subcategory_class'>,
diff --git a/src/sage/categories/sets_cat.py b/src/sage/categories/sets_cat.py
index 51eb9b14453..d8d278e80c5 100644
--- a/src/sage/categories/sets_cat.py
+++ b/src/sage/categories/sets_cat.py
@@ -136,9 +136,9 @@ class Sets(Category_singleton):
         <class 'sage.categories.examples.sets_cat.PrimeNumbers_Inherits'>
         <class 'sage.categories.examples.sets_cat.PrimeNumbers_Abstract'>
         <class 'sage.structure.unique_representation.UniqueRepresentation'>
+        <class 'sage.misc.fast_methods.WithEqualityById'>
         <class 'sage.structure.unique_representation.CachedRepresentation'>
         <class 'sage.structure.unique_representation.WithPicklingByInitArgs'>
-        <class 'sage.misc.fast_methods.WithEqualityById'>
         <class 'sage.structure.parent.Parent'>
         <class 'sage.structure.category_object.CategoryObject'>
         <class 'sage.structure.sage_object.SageObject'>
diff --git a/src/sage/combinat/root_system/cartan_type.py b/src/sage/combinat/root_system/cartan_type.py
index e4526d5f079..8899b07bf21 100644
--- a/src/sage/combinat/root_system/cartan_type.py
+++ b/src/sage/combinat/root_system/cartan_type.py
@@ -3069,39 +3069,3 @@ def __getitem__(self, i):
             raise IndexError("index out of range")
 
     options = CartanType.options
-
-##############################################################################
-# For backward compatibility
-
-
-class CartanType_simple_finite:
-    def __setstate__(self, dict):
-        """
-        Implements the unpickling of Cartan types pickled by Sage <= 4.0.
-
-        EXAMPLES:
-
-        This is the pickle for CartanType(["A", 4])::
-
-            sage: pg_CartanType_simple_finite = unpickle_global('sage.combinat.root_system.cartan_type', 'CartanType_simple_finite')
-            sage: si1 = unpickle_newobj(pg_CartanType_simple_finite, ())
-            sage: from sage.misc.fpickle import unpickleModule
-            sage: pg_make_integer = unpickle_global('sage.rings.integer', 'make_integer')
-            sage: si2 = pg_make_integer('4')
-            sage: unpickle_build(si1, {'tools':unpickleModule('sage.combinat.root_system.type_A'), 't':['A', si2], 'letter':'A', 'n':si2})
-
-            sage: si1
-            ['A', 4]
-            sage: si1.dynkin_diagram()                                                  # needs sage.graphs
-            O---O---O---O
-            1   2   3   4
-            A4
-
-        This is quite hacky; in particular unique representation is not preserved::
-
-            sage: si1 == CartanType(["A", 4]) # todo: not implemented
-            True
-        """
-        T = CartanType([dict['letter'], dict['n']])
-        self.__class__ = T.__class__
-        self.__dict__ = T.__dict__
diff --git a/src/sage/structure/unique_representation.py b/src/sage/structure/unique_representation.py
index 7f769522caf..0a7632a543d 100644
--- a/src/sage/structure/unique_representation.py
+++ b/src/sage/structure/unique_representation.py
@@ -1201,7 +1201,7 @@ def _clear_cache_(cls):
             del cache[k]
 
 
-class UniqueRepresentation(CachedRepresentation, WithEqualityById):
+class UniqueRepresentation(WithEqualityById, CachedRepresentation):
     r"""
     Classes derived from ``UniqueRepresentation`` inherit a unique
     representation behavior for their instances.