BUG: Fix TypeError in assert_index_equal when comparing CategoricalIndex with check_categorical=True and exact=False (#61941)

Author: Aniketsy

doc/source/whatsnew/v3.0.0.rst

@@ -933,6 +933,7 @@ Bug fixes
 Categorical
 ^^^^^^^^^^^
 - Bug in :func:`Series.apply` where ``nan`` was ignored for :class:`CategoricalDtype` (:issue:`59938`)
+- Bug in :func:`testing.assert_index_equal` raising ``TypeError`` instead of ``AssertionError`` for incomparable ``CategoricalIndex`` when ``check_categorical=True`` and ``exact=False`` (:issue:`61935`)
 - Bug in :meth:`Categorical.astype` where ``copy=False`` would still trigger a copy of the codes (:issue:`62000`)
 - Bug in :meth:`DataFrame.pivot` and :meth:`DataFrame.set_index` raising an ``ArrowNotImplementedError`` for columns with pyarrow dictionary dtype (:issue:`53051`)
 - Bug in :meth:`Series.convert_dtypes` with ``dtype_backend="pyarrow"`` where empty :class:`CategoricalDtype` :class:`Series` raised an error or got converted to ``null[pyarrow]`` (:issue:`59934`)

pandas/_testing/asserters.py

@@ -325,7 +325,17 @@ def _check_types(left, right, obj: str = "Index") -> None:
     # skip exact index checking when `check_categorical` is False
     elif check_exact and check_categorical:
         if not left.equals(right):
-            mismatch = left._values != right._values
+            # _values compare can raise TypeError (non-comparable
+            # categoricals (GH#61935)
+            try:
+                mismatch = left._values != right._values
+            except TypeError:
+                raise_assert_detail(
+                    obj,
+                    "types are not comparable (non-matching categorical categories)",
+                    left,
+                    right,
+                )
 
             if not isinstance(mismatch, np.ndarray):
                 mismatch = cast("ExtensionArray", mismatch).fillna(True)

pandas/tests/util/test_assert_index_equal.py

@@ -317,3 +317,11 @@ def test_assert_multi_index_dtype_check_categorical(check_categorical):
             tm.assert_index_equal(idx1, idx2, check_categorical=check_categorical)
     else:
         tm.assert_index_equal(idx1, idx2, check_categorical=check_categorical)
+
+
+def test_assert_index_equal_categorical_incomparable_categories():
+    # GH#61935
+    left = Index([1, 2, 3], name="a", dtype="category")
+    right = Index([1, 2, 6], name="a", dtype="category")
+    with pytest.raises(AssertionError, match="types are not comparable"):
+        tm.assert_index_equal(left, right, check_categorical=True, exact=False)