id,node_id,number,title,user,state,locked,assignee,milestone,comments,created_at,updated_at,closed_at,author_association,active_lock_reason,draft,pull_request,body,reactions,performed_via_github_app,state_reason,repo,type
340316108,MDU6SXNzdWUzNDAzMTYxMDg=,2280,string coords are converted to object dtype when using MultiIndex / stacking,1034035,closed,0,,,5,2018-07-11T16:26:12Z,2022-09-27T12:12:06Z,2022-09-27T12:12:05Z,NONE,,,,"#### Code Sample

```python
import xarray as xr
import pandas as pd

indx = pd.MultiIndex.from_arrays([['1', '2', '1', '2'],
                                  ['100', '100', '200', '200']],
                                 names=['a', 'b'])
# MultiIndex(levels=[['1', '2'], ['100', '200']],
#            labels=[[0, 1, 0, 1], [0, 0, 1, 1]],
#            names=['a', 'b'])

tst = xr.DataArray(data=np.random.random((4)), coords=[('ab', indx)])
# <xarray.DataArray (ab: 4)>
# array([0.754308, 0.268363, 0.799407, 0.513185])
# Coordinates:
#   * ab       (ab) MultiIndex
#   - a        (ab) object '1' '2' '1' '2'
#   - b        (ab) object '100' '100' '200' '200'

tst2 = xr.DataArray(data=np.random.random((2,2)),
                    coords=[('a', ['1', '2']), ('b', ['100', '200'])])
# <xarray.DataArray (a: 2, b: 2)>
# array([[0.854303, 0.179755],
#        [0.463453, 0.478913]])
# Coordinates:
#   * a        (a) <U1 '1' '2'
#   * b        (b) <U3 '100' '200'

tst2.stack(ab=('a', 'b'))
# <xarray.DataArray (ab: 4)>
# array([0.854303, 0.179755, 0.463453, 0.478913])
# Coordinates:
#   * ab       (ab) MultiIndex
#   - a        (ab) object '1' '1' '2' '2'
#   - b        (ab) object '100' '200' '100' '200'
```
#### Problem description

The dtype for `a` and `b` in `tst` and `tst2.stack()` is `object` rather than some string dtype.

#### Expected Output

A string dtype for `a` and `b`.

#### Output of ``xr.show_versions()``

<details>
# Paste the output here xr.show_versions() here
INSTALLED VERSIONS
------------------
commit: None
python: 3.6.5.final.0
python-bits: 64
OS: Linux
OS-release: 4.15.0-24-generic
machine: x86_64
processor: x86_64
byteorder: little
LC_ALL: None
LANG: en_US.UTF-8
LOCALE: en_US.UTF-8

xarray: 0.10.7
pandas: 0.23.1
numpy: 1.14.5
scipy: 1.1.0
netCDF4: 1.4.0
h5netcdf: 0.6.1
h5py: 2.8.0
Nio: None
zarr: None
bottleneck: 1.2.1
cyordereddict: None
dask: 0.18.1
distributed: 1.22.0
matplotlib: 2.2.2
cartopy: None
seaborn: 0.8.1
setuptools: 39.2.0
pip: 9.0.3
conda: 4.5.5
pytest: 3.6.2
IPython: 6.4.0
sphinx: 1.7.5
</details>
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