In [52]:
import pandas as pd

a = pd.Series(['a','b','c'],dtype="category")
b = pd.Series(['a','b','c'],dtype="object")
c = pd.Series(['a','b','cc'],dtype="object")

In [54]:

a==b

---------------------------------------------------------------------------
TypeError                                 Traceback (most recent call last)
...
TypeError: Cannot compare a Categorical for op <built-in function eq> with type <class         'numpy.ndarray'>. If you want to compare values, use 'series <op> np.asarray(cat)'.

In [59]:
A = pd.DataFrame({'A':a,'B':[1,2,3]})
B = pd.DataFrame({'A':b,'C':[4,5,6]})
print(A.merge(B,on='A'))
   A  B  C
0  a  1  4
1  b  2  5
2  c  3  6