Karak du Vide
Mages captured by the Inquisition are brought to their island stronghold south of Artorius: Karak du Vide, the Castle of the Void. Once a prison colony of the Empire, it was dedicated to mage-prisoners some time after the formation of the Inquisition. Since then, it has developed into an intimidating, angular black fortress surrounding the entire island commune. Few have ever seen what lies behind those black walls and returned to speak of it, save Imperial inspectors and the Inquisitors themselves.
Karak du Vide is divided into several main sections. Within the walls is the village, a community in which peaceful mages are allowed to interact and live out their lives so long as they do not cast any disruptive spells. This community actually works as an incentive; some mages have willingly turned themselves in to the Inquisition just to live there with others who share their gift. The walls, towers, and the main keep belong to the Inquisitors themselves. They have their own barracks, library, temple, stables, docks, etc. - a self-sustaining community that also supports the village. Under the castle lies the dungeon, which consists of several sections as well: the prison section, for mages who refuse to live by the rules of the village community and thus have to be segregated from it... and the lower dungeon, where extremely dangerous mages are kept in solitary confinement, and sometimes, it is said, are subjected to strange experiments as the Inquisitors try to better understand the nature of magic.
The Inquisitors have thus built up the largest storehouse of Arcane knowledge to exist anywhere outside of the secret mage tower in the Jagged Edge. Very, very few are allowed access to it besides the Inquisitors themselves.
Finally, it is noteworthy that the Inquisition only has jurisdiction over human mages. Though there are some elves, dwarves, and other creatures imprisoned in their island stronghold, non-humans are usually deported back to their homelands... or simply executed, especially if their kin do not want them back.