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Showing content from https://github.com/pandas-dev/pandas/issues/16014 below:

Unordered Categorical should ignore order in comparisons? · Issue #16014 · pandas-dev/pandas · GitHub

I think that when comparing two unordered categorical-dtyped series with categories which differ only by ordered should compare equal

In [1]: import pandas as pd
c
In [2]: c1 = pd.Series(pd.Categorical(['a', 'b']))

In [3]: c2 = pd.Series(pd.Categorical(['a', 'b'], categories=['b', 'a']))

In [4]: c1
Out[4]:
0    a
1    b
dtype: category
Categories (2, object): [a, b]

In [5]: c2
Out[5]:
0    a
1    b
dtype: category
Categories (2, object): [b, a]

In [6]: c1 == c2

---------------------------------------------------------------------------
TypeError                                 Traceback (most recent call last)
<ipython-input-6-d8d43a43a02a> in <module>()
----> 1 c1 == c2

/Users/taugspurger/Envs/statsmodels-dev/lib/python3.6/site-packages/pandas/core/ops.py in wrapper(self, other, axis)
    811                 msg = 'Can only compare identically-labeled Series objects'
    812                 raise ValueError(msg)
--> 813             return self._constructor(na_op(self.values, other.values),
    814                                      index=self.index, name=name)
    815         elif isinstance(other, pd.DataFrame):  # pragma: no cover

/Users/taugspurger/Envs/statsmodels-dev/lib/python3.6/site-packages/pandas/core/ops.py in na_op(x, y)
    752         # in either operand
    753         if is_categorical_dtype(x):
--> 754             return op(x, y)
    755         elif is_categorical_dtype(y) and not isscalar(y):
    756             return op(y, x)

/Users/taugspurger/Envs/statsmodels-dev/lib/python3.6/site-packages/pandas/core/categorical.py in f(self, other)
     55             if ((len(self.categories) != len(other.categories)) or
     56                     not ((self.categories == other.categories).all())):
---> 57                 raise TypeError("Categoricals can only be compared if "
     58                                 "'categories' are the same")
     59             if not (self.ordered == other.ordered):

TypeError: Categoricals can only be compared if 'categories' are the same

I think this should return True. Unordered categories shouldn't care about the order :)

cc @JanSchulz thoughts?

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