Merge branch 'cat_eq_string' into string_dtype_tests

# Conflicts:
#	doc/source/whatsnew/v2.1.2.rst

Author: phofl

doc/source/whatsnew/v2.1.2.rst

@@ -25,6 +25,7 @@ Bug fixes
 - Fixed bug in :meth:`DataFrame.interpolate` raising incorrect error message (:issue:`55347`)
 - 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`)
+- Fixed bug in :meth:`Categorical.equals` if other has arrow backed string dtype (:issue:`TODO`)
 - Fixed bug in :meth:`Series.rank` for ``string[pyarrow_numpy]`` dtype (:issue:`TODO`)
 
 .. ---------------------------------------------------------------------------

pandas/core/arrays/arrow/array.py

@@ -32,6 +32,7 @@
 
 from pandas.core.dtypes.cast import can_hold_element
 from pandas.core.dtypes.common import (
+    CategoricalDtype,
     is_array_like,
     is_bool_dtype,
     is_integer,
@@ -627,7 +628,9 @@ 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#
+        idx = CategoricalIndex(list("abc"), name="B")
+        other = Index(["a", "b", "c"], name="B", dtype=any_string_dtype)
+        assert idx.equals(other)