Does the imam need to make a separate intention for the women following him?

The general intention the imam makes for leading the prayer also includes women. Therefore, he does not need to make a separate intention specifically for women. However, according to the Hanafi school, if a man is praying alone without the intention of leading, a woman cannot join him later as a follower. (see Ibn Abidin, Radd al-Muhtar, 1/575-576)

According to the Shafi'i school, it is not obligatory but recommended (mustahabb) for the imam to intend to lead both men and women. (Shirbini, Mughni al-Muhtaj, 1/502) Therefore, a woman may join a man who is already praying alone as a follower.

Source: T.C. Diyanet İşleri Başkanlığı, Din İşleri Yüksek Kurulu