BUG: categorical dtype equality for level in different type (#55486)

* BUG: categorical dtype equality for level in different type

* BUG: categorical dtype equality for level in different type - Comments#1

doc/source/whatsnew/v2.2.0.rst

@@ -285,6 +285,7 @@ Bug fixes
 Categorical
 ^^^^^^^^^^^
 - :meth:`Categorical.isin` raising ``InvalidIndexError`` for categorical containing overlapping :class:`Interval` values (:issue:`34974`)
+- Bug in :meth:`CategoricalDtype.__eq__` returning false for unordered categorical data with mixed types (:issue:`55468`)
 -
 
 Datetimelike

pandas/core/dtypes/dtypes.py

@@ -456,7 +456,7 @@ def __eq__(self, other: object) -> bool:
 
             # With object-dtype we need a comparison that identifies
             #  e.g. int(2) as distinct from float(2)
-            return hash(self) == hash(other)
+            return set(left) == set(right)
 
     def __repr__(self) -> str_type:
         if self.categories is None:

pandas/tests/dtypes/test_dtypes.py

@@ -917,6 +917,24 @@ def test_equal_but_different(self):
         assert c1 is not c2
         assert c1 != c2
 
+    def test_equal_but_different_mixed_dtypes(self):
+        c1 = CategoricalDtype([1, 2, "3"])
+        c2 = CategoricalDtype(["3", 1, 2])
+        assert c1 is not c2
+        assert c1 == c2
+
+    def test_equal_empty_ordered(self):
+        c1 = CategoricalDtype([], ordered=True)
+        c2 = CategoricalDtype([], ordered=True)
+        assert c1 is not c2
+        assert c1 == c2
+
+    def test_equal_empty_unordered(self):
+        c1 = CategoricalDtype([])
+        c2 = CategoricalDtype([])
+        assert c1 is not c2
+        assert c1 == c2
+
     @pytest.mark.parametrize("v1, v2", [([1, 2, 3], [1, 2, 3]), ([1, 2, 3], [3, 2, 1])])
     def test_order_hashes_different(self, v1, v2):
         c1 = CategoricalDtype(v1, ordered=False)