BUG: fix bug where appending unordered CategoricalIndex variables overrides index

doc/source/whatsnew/v1.5.0.rst

@@ -407,7 +407,6 @@ upon serialization. (Related issue :issue:`12997`)
     # Roundtripping now works
     pd.read_json(a.to_json(date_format='iso'), typ="series").index == a.index
 
-
 .. _whatsnew_150.notable_bug_fixes.groupby_value_counts_categorical:
 
 DataFrameGroupBy.value_counts with non-grouping categorical columns and ``observed=True``
@@ -888,8 +887,9 @@ Bug fixes
 
 Categorical
 ^^^^^^^^^^^
-- Bug in :meth:`Categorical.view` not accepting integer dtypes (:issue:`25464`)
-- Bug in :meth:`CategoricalIndex.union` when the index's categories are integer-dtype and the index contains ``NaN`` values incorrectly raising instead of casting to ``float64`` (:issue:`45362`)
+- Bug in :meth:`.Categorical.view` not accepting integer dtypes (:issue:`25464`)
+- Bug in :meth:`.CategoricalIndex.union` when the index's categories are integer-dtype and the index contains ``NaN`` values incorrectly raising instead of casting to ``float64`` (:issue:`45362`)
+- Bug in :meth:`DataFrame.concat` when concatenating two (or more) unordered ``CategoricalIndex`` variables, whose categories are permutations, yields incorrect index values (:issue:`24845`)
 
 Datetimelike
 ^^^^^^^^^^^^

pandas/core/indexes/category.py

@@ -573,13 +573,14 @@ def map(self, mapper):
     def _concat(self, to_concat: list[Index], name: Hashable) -> Index:
         # if calling index is category, don't check dtype of others
         try:
-            codes = np.concatenate([self._is_dtype_compat(c).codes for c in to_concat])
+            cat = Categorical._concat_same_type(
+                [self._is_dtype_compat(c) for c in to_concat]
+            )
         except TypeError:
             # not all to_concat elements are among our categories (or NA)
             from pandas.core.dtypes.concat import concat_compat
 
             res = concat_compat([x._values for x in to_concat])
             return Index(res, name=name)
         else:
-            cat = self._data._from_backing_data(codes)
             return type(self)._simple_new(cat, name=name)

pandas/tests/reshape/concat/test_categorical.py

@@ -238,3 +238,19 @@ def test_categorical_missing_from_one_frame(self):
             index=[0, 1, 2, 0, 1, 2],
         )
         tm.assert_frame_equal(result, expected)
+
+    def test_concat_categorical_same_categories_different_order(self):
+        # https://github.com/pandas-dev/pandas/issues/24845
+
+        c1 = pd.CategoricalIndex(["a", "a"], categories=["a", "b"], ordered=False)
+        c2 = pd.CategoricalIndex(["b", "b"], categories=["b", "a"], ordered=False)
+        c3 = pd.CategoricalIndex(
+            ["a", "a", "b", "b"], categories=["a", "b"], ordered=False
+        )
+
+        df1 = DataFrame({"A": [1, 2]}, index=c1)
+        df2 = DataFrame({"A": [3, 4]}, index=c2)
+
+        result = pd.concat((df1, df2))
+        expected = DataFrame({"A": [1, 2, 3, 4]}, index=c3)
+        tm.assert_frame_equal(result, expected)