Locations and uses
Behind the locked door in the Cathedral that requires a different badge is a room. On the east side of that room is another locked door. Like the door before, this one can be unlocked by lockpicking or by use of this badge. Morpheus carries two of this type of badge.
Upon arrival at the Cathedral, the task is to go through a staircase in the back of the main room. However, the door leading to that room is locked. To get there, this badge is needed (or again, the door can be lockpicked). Most of the Children in the main room, like Laura and Lasher, carry one.