Inequalities on pandas column

I have a pandas dataframe, and I would like to create a new column based on an existing column and certain inequalities. For example, let

df=pd.DataFrame({'a':[1,2,3,4,5,6,7],'b':[3,6,4,2,7,7,1]})

so df looks like

    a   b
0   1   3
1   2   6
2   3   4
3   4   2
4   5   7
5   6   7
6   7   1

I would like to add a new column, res, that equals 0 if the corresponding value in a is smaller than 2, 1 if the corresponding value in a is at least 2 and smaller than 4, and 2 otherwise. So I would like to get

    a   b   res
0   1   3   0
1   2   6   1
2   3   4   1
3   4   2   2
4   5   7   2
5   6   7   2
6   7   1   2

So far I have been doing this by using apply as follows:

def f(x):
    if x['a']<2:
        return 0
    elif x['a']>=2 and x['a']<4:
        return 1
    else:
        return 2
df['res']=df.apply(f,axis=1)

but I was wondering if there is a more direct way, or some specific pandas method that can enable me to do that.