diff --git a/pandas/core/base.py b/pandas/core/base.py
index f30430dd394ca..18fc76fe79a5a 100644
--- a/pandas/core/base.py
+++ b/pandas/core/base.py
@@ -24,6 +24,7 @@
     DtypeObj,
     IndexLabel,
     Shape,
+    final,
 )
 from pandas.compat import PYPY
 from pandas.compat.numpy import function as nv
@@ -933,12 +934,8 @@ def _map_values(self, mapper, na_action=None):
                 # use the built in categorical series mapper which saves
                 # time by mapping the categories instead of all values
 
-                # error: Incompatible types in assignment (expression has type
-                # "Categorical", variable has type "IndexOpsMixin")
-                self = cast("Categorical", self)  # type: ignore[assignment]
-                # error: Item "ExtensionArray" of "Union[ExtensionArray, Any]" has no
-                # attribute "map"
-                return self._values.map(mapper)  # type: ignore[union-attr]
+                cat = cast("Categorical", self._values)
+                return cat.map(mapper)
 
             values = self._values
 
@@ -955,8 +952,7 @@ def _map_values(self, mapper, na_action=None):
                 raise NotImplementedError
             map_f = lambda values, f: values.map(f)
         else:
-            # error: "IndexOpsMixin" has no attribute "astype"
-            values = self.astype(object)._values  # type: ignore[attr-defined]
+            values = self._values.astype(object)
             if na_action == "ignore":
                 map_f = lambda values, f: lib.map_infer_mask(
                     values, f, isna(values).view(np.uint8)
@@ -1327,9 +1323,10 @@ def searchsorted(self, value, side="left", sorter=None) -> np.ndarray:
         return algorithms.searchsorted(self._values, value, side=side, sorter=sorter)
 
     def drop_duplicates(self, keep="first"):
-        duplicated = self.duplicated(keep=keep)
+        duplicated = self._duplicated(keep=keep)
         # error: Value of type "IndexOpsMixin" is not indexable
         return self[~duplicated]  # type: ignore[index]
 
-    def duplicated(self, keep: Union[str, bool] = "first") -> np.ndarray:
+    @final
+    def _duplicated(self, keep: Union[str, bool] = "first") -> np.ndarray:
         return duplicated(self._values, keep=keep)
diff --git a/pandas/core/indexes/base.py b/pandas/core/indexes/base.py
index af3315dd2ade6..fc4eeebc86642 100644
--- a/pandas/core/indexes/base.py
+++ b/pandas/core/indexes/base.py
@@ -2663,7 +2663,7 @@ def duplicated(self, keep: Union[str_t, bool] = "first") -> np.ndarray:
 
         Returns
         -------
-        numpy.ndarray
+        np.ndarray[bool]
 
         See Also
         --------
@@ -2699,7 +2699,7 @@ def duplicated(self, keep: Union[str_t, bool] = "first") -> np.ndarray:
         if self.is_unique:
             # fastpath available bc we are immutable
             return np.zeros(len(self), dtype=bool)
-        return super().duplicated(keep=keep)
+        return self._duplicated(keep=keep)
 
     def _get_unique_index(self: _IndexT) -> _IndexT:
         """
diff --git a/pandas/core/indexes/multi.py b/pandas/core/indexes/multi.py
index 76878d0a0b82a..fedb955ce83b9 100644
--- a/pandas/core/indexes/multi.py
+++ b/pandas/core/indexes/multi.py
@@ -1614,12 +1614,16 @@ def _inferred_type_levels(self) -> List[str]:
         return [i.inferred_type for i in self.levels]
 
     @doc(Index.duplicated)
-    def duplicated(self, keep="first"):
+    def duplicated(self, keep="first") -> np.ndarray:
         shape = map(len, self.levels)
         ids = get_group_index(self.codes, shape, sort=False, xnull=False)
 
         return duplicated_int64(ids, keep)
 
+    # error: Cannot override final attribute "_duplicated"
+    # (previously declared in base class "IndexOpsMixin")
+    _duplicated = duplicated  # type: ignore[misc]
+
     def fillna(self, value=None, downcast=None):
         """
         fillna is not implemented for MultiIndex
@@ -2216,11 +2220,7 @@ def drop(self, codes, level=None, errors="raise"):
 
         if not isinstance(codes, (np.ndarray, Index)):
             try:
-                # error: Argument "dtype" to "index_labels_to_array" has incompatible
-                # type "Type[object]"; expected "Union[str, dtype[Any], None]"
-                codes = com.index_labels_to_array(
-                    codes, dtype=object  # type: ignore[arg-type]
-                )
+                codes = com.index_labels_to_array(codes, dtype=np.dtype("object"))
             except ValueError:
                 pass
 
diff --git a/pandas/core/series.py b/pandas/core/series.py
index 27042f7de9dc1..641a57a554a9b 100644
--- a/pandas/core/series.py
+++ b/pandas/core/series.py
@@ -1874,7 +1874,7 @@ def mode(self, dropna=True) -> Series:
         # TODO: Add option for bins like value_counts()
         return algorithms.mode(self, dropna=dropna)
 
-    def unique(self):
+    def unique(self) -> ArrayLike:
         """
         Return unique values of Series object.
 
@@ -2020,9 +2020,7 @@ def drop_duplicates(self, keep="first", inplace=False) -> Optional[Series]:
         else:
             return result
 
-    # error: Return type "Series" of "duplicated" incompatible with return type
-    # "ndarray" in supertype "IndexOpsMixin"
-    def duplicated(self, keep="first") -> Series:  # type: ignore[override]
+    def duplicated(self, keep="first") -> Series:
         """
         Indicate duplicate Series values.
 
@@ -2043,7 +2041,7 @@ def duplicated(self, keep="first") -> Series:  # type: ignore[override]
 
         Returns
         -------
-        Series
+        Series[bool]
             Series indicating whether each value has occurred in the
             preceding values.
 
@@ -2098,7 +2096,7 @@ def duplicated(self, keep="first") -> Series:  # type: ignore[override]
         4     True
         dtype: bool
         """
-        res = base.IndexOpsMixin.duplicated(self, keep=keep)
+        res = self._duplicated(keep=keep)
         result = self._constructor(res, index=self.index)
         return result.__finalize__(self, method="duplicated")