a = pd.Index(['a', 'b', 'a'])
b = pd.Index(['a', 'b', 'a'], dtype='category')
a.str.cat(b)
# Index(['aa', 'bb', 'aa'], dtype='object')
b.str.cat(a)
# AttributeError: Can only use .str accessor with string values (i.e. inferred_type is 'string', 'unicode' or 'mixed')