BUG: Categorical dtype in MultiIndex levels is lost during set operations (difference, union, intersection,...)

[tscheburaschka]

• I have checked that this issue has not already been reported.

• I have confirmed this bug exists on the latest version of pandas.

• (optional) I have confirmed this bug exists on the master branch of pandas.

---

Coming from here, I tried my issue on current HEAD@master and the erroneous behaviour still persists.

Code Sample, a copy-pastable example

import pandas as pd

cat = pd.CategoricalDtype(categories=[1, 2, 3, 4])
df = pd.DataFrame({'a': [1, 2, 3, 4, 3, 2, 1], 'b': [4, 3, 2, 3, 1, 2, 3]}, dtype=cat)

# flat categorical index, no MultiIndex
df_cat = df.set_index('a', drop=False)

diff_ind = df_cat.index.difference(df_cat.head(3).index)
print(diff_ind.dtype)  # -> category

union_ind = df_cat.index.union(df_cat.head(3).index)
print(union_ind.dtype)  # -> category


# same set operations on MultiIndex, categorical gets lost
df_cat_multi = df.set_index(['a', 'b'], drop=False)
# just make sure, we have a categorical in the first place
print(df_cat_multi.index.get_level_values(0).dtype)  # -> category
print(df_cat_multi.index.get_level_values(1).dtype)  # -> category

diff_multi_ind = df_cat_multi.index.difference(df_cat_multi.head(3).index)
print(diff_multi_ind.get_level_values(0).dtype)  # -> int64
print(diff_multi_ind.get_level_values(1).dtype)  # -> int64

union_multi_ind = df_cat_multi.index.union(df_cat_multi.head(3).index)
print(union_multi_ind.get_level_values(0).dtype)  # -> int64
print(union_multi_ind.get_level_values(1).dtype)  # -> int64

Problem description

In contrast to set operations involving flat categorical indices, the same operations on multi-indices with categorical level values revert the result back to the underlying datatype.

Expected Output

The set-operations on multi-indices should preserve the categorical dtype of level values.

Output of pd.show_versions()

INSTALLED VERSIONS

commit : ab687ae
python : 3.8.6.final.0
python-bits : 64
OS : Windows
OS-release : 10
Version : 10.0.19041
machine : AMD64
processor : Intel64 Family 6 Model 94 Stepping 3, GenuineIntel
byteorder : little
LC_ALL : None
LANG : None
LOCALE : de_DE.cp1252

pandas : 1.3.0.dev0+849.gab687aec38
numpy : 1.19.5
pytz : 2021.1
dateutil : 2.8.1
pip : 21.0.1
setuptools : 53.1.0
Cython : 0.29.22
pytest : None
hypothesis : None
sphinx : None
blosc : None
feather : None
xlsxwriter : None
lxml.etree : None
html5lib : None
pymysql : None
psycopg2 : None
jinja2 : None
IPython : None
pandas_datareader: None
bs4 : None
bottleneck : None
fsspec : None
fastparquet : None
gcsfs : None
matplotlib : None
numexpr : None
odfpy : None
openpyxl : None
pandas_gbq : None
pyarrow : None
pyxlsb : None
s3fs : None
scipy : None
sqlalchemy : None
tables : None
tabulate : None
xarray : None
xlrd : None
xlwt : None
numba : None

[mzeitlin11]

Thanks for the detailed report, @tscheburaschka! Investigations to fix are certainly welcome!

[lukemanley]

This appears to be fixed on main. Could use a test.