CLN: use _values_for_argsort in fewer places

pandas/core/algorithms.py

@@ -616,7 +616,7 @@ def factorize(
     values = _ensure_arraylike(values)
     original = values
 
-    if is_extension_array_dtype(values):
+    if is_extension_array_dtype(values.dtype):
         values = extract_array(values)
         codes, uniques = values.factorize(na_sentinel=na_sentinel)
         dtype = original.dtype

pandas/core/arrays/categorical.py

@@ -370,7 +370,7 @@ def __init__(
             # we're inferring from values
             dtype = CategoricalDtype(categories, dtype.ordered)
 
-        elif is_categorical_dtype(values):
+        elif is_categorical_dtype(values.dtype):
             old_codes = (
                 values._values.codes if isinstance(values, ABCSeries) else values.codes
             )

pandas/core/indexes/base.py

@@ -3597,12 +3597,8 @@ def _join_non_unique(self, other, how="left", return_indexers=False):
         # We only get here if dtypes match
         assert self.dtype == other.dtype
 
-        if is_extension_array_dtype(self.dtype):
-            lvalues = self._data._values_for_argsort()
-            rvalues = other._data._values_for_argsort()
-        else:
-            lvalues = self._values
-            rvalues = other._values
+        lvalues = self._get_engine_target()
+        rvalues = other._get_engine_target()
 
         left_idx, right_idx = _get_join_indexers(
             [lvalues], [rvalues], how=how, sort=True
@@ -3774,12 +3770,8 @@ def _join_monotonic(self, other, how="left", return_indexers=False):
             else:
                 return ret_index
 
-        if is_extension_array_dtype(self.dtype):
-            sv = self._data._values_for_argsort()
-            ov = other._data._values_for_argsort()
-        else:
-            sv = self._values
-            ov = other._values
+        sv = self._get_engine_target()
+        ov = other._get_engine_target()
 
         if self.is_unique and other.is_unique:
             # We can perform much better than the general case

pandas/core/indexes/extension.py

@@ -232,6 +232,9 @@ def __array__(self, dtype=None) -> np.ndarray:
         return np.asarray(self._data, dtype=dtype)
 
     def _get_engine_target(self) -> np.ndarray:
+        # NB: _values_for_argsort happens to match the desired engine targets
+        #  for all of our existing EA-backed indexes, but in general
+        #  cannot be relied upon to exist.
         return self._data._values_for_argsort()
 
     @doc(Index.dropna)