Well, except for the Hagia Sophia, which was converted into a mosque (forcibly, may I add) many centuries ago.
The style is not important, actually. The word "cathedral" comes from the Latin word "cathedra," which means "chair" in English. That is because the bishop's chair - or seat - is actually at that church, meaning that he is the permanent bishop of that geographical diocese. If you go into a Catholic cathedral, you will see an actual chair where the bishop of that diocese sits when he is there. Currently it is usually on the congregation's left, behind the lectern that used to be known as the "Gospel side" of the altar. I assume the same is true for Anglicans.
The 'Agia Sophia no longer is a mosque.
It was converted into a museum under Kemal Ataturk.