BUG: unstack doesn't preserve categorical dtype

Code Sample, a copy-pastable example if possible

idx = pd.MultiIndex.from_product([['A'], [0, 1]])
df = pd.DataFrame({'cat': pd.Categorical(['a', 'b'])}, index=idx)
df
Out[19]: 
    cat
A 0   a
  1   b

df.unstack()
Out[21]: 
  cat   
    0  1
A   a  b

Categorical dtype is lost:

df.unstack().dtypes
Out[22]: 
cat  0    object
     1    object
dtype: object

But it works ok for a Series:

df['cat'].unstack()
Out[24]: 
   0  1
A  a  b
df['cat'].unstack().dtypes
Out[25]: 
0    category
1    category
dtype: object

Expected Output

I believe df.unstack() should preserve categorical dtypes as df['cat'].unstack() does.

output of pd.show_versions()

pd.show_versions()

INSTALLED VERSIONS
------------------
commit: 5d791cc7d955c0b074ad602eb03fa32bd3e17503
python: 3.5.1.final.0
python-bits: 64
OS: Linux
OS-release: 4.1.20-1
machine: x86_64
processor: Intel(R)_Core(TM)_i5-2520M_CPU_@_2.50GHz
byteorder: little
LC_ALL: None
LANG: en_US.UTF-8
LOCALE: en_US.UTF-8

pandas: 0.18.1+368.g5d791cc
nose: 1.3.7
pip: 8.1.2
setuptools: 21.0.0
Cython: 0.24
numpy: 1.11.0
...

This is related to #13743 (and PR #13854), though a bit more difficult to fix.

[mroeschke]

Sorry don’t have time for a call. But the output should be as noted in https://github.com/pandas-dev/pandas/issues/14018#issuecomment-650831541

[mroeschke]

Sure @Abhispy007. pandas/tests/frame/tests_reshape.py would be a good place this test