BUG: eq not implemented for categorical and arrow backed strings (#55364)

Author: phofl

doc/source/whatsnew/v2.1.2.rst

@@ -22,6 +22,7 @@ Fixed regressions
 
 Bug fixes
 ~~~~~~~~~
+- Fixed bug in :meth:`Categorical.equals` if other has arrow backed string dtype (:issue:`55364`)
 - Fixed bug in :meth:`DataFrame.idxmin` and :meth:`DataFrame.idxmax` raising for arrow dtypes (:issue:`55368`)
 - Fixed bug in :meth:`DataFrame.resample` not respecting ``closed`` and ``label`` arguments for :class:`~pandas.tseries.offsets.BusinessDay` (:issue:`55282`)
 - Fixed bug in :meth:`DataFrame.resample` where bin edges were not correct for :class:`~pandas.tseries.offsets.BusinessDay` (:issue:`55281`)

pandas/core/arrays/arrow/array.py

@@ -35,6 +35,7 @@
     infer_dtype_from_scalar,
 )
 from pandas.core.dtypes.common import (
+    CategoricalDtype,
     is_array_like,
     is_bool_dtype,
     is_integer,
@@ -631,7 +632,9 @@ def __setstate__(self, state) -> None:
 
     def _cmp_method(self, other, op):
         pc_func = ARROW_CMP_FUNCS[op.__name__]
-        if isinstance(other, (ArrowExtensionArray, np.ndarray, list, BaseMaskedArray)):
+        if isinstance(
+            other, (ArrowExtensionArray, np.ndarray, list, BaseMaskedArray)
+        ) or isinstance(getattr(other, "dtype", None), CategoricalDtype):
             result = pc_func(self._pa_array, self._box_pa(other))
         elif is_scalar(other):
             try:

pandas/tests/indexes/categorical/test_equals.py

@@ -88,3 +88,9 @@ def test_equals_multiindex(self):
         ci = mi.to_flat_index().astype("category")
 
         assert not ci.equals(mi)
+
+    def test_equals_string_dtype(self, any_string_dtype):
+        # GH#55364
+        idx = CategoricalIndex(list("abc"), name="B")
+        other = Index(["a", "b", "c"], name="B", dtype=any_string_dtype)
+        assert idx.equals(other)