Purgatorium is a location within the Phantom Field that debuted in BlazBlue: Central Fiction. It is the stage of Nine the Phantom.
After freeing herself from the control of Izanami, Nine used Purgatorium as a location to test the strengths of the Chosen who had been absorbed into the Embryo. She took nearly all the Chosen to this location to fight them, and pointed them to Izanami afterwards; as this happened during a Continuum Shift, these possibilities were erased. Instead, the only possibility that became reality was when she summoned Ragna the Bloodedge to Purgatorium and bested him there, but sent him back into the real world afterwards.
Purgatorium is set inside the Phantom Field, an area created by Nobody. The floor is tiled, with each tile having a large glowing rune in its center - dotted across these tiles are numerous skulls. It appears to be set inside a large cave, as there is no sunlight and the arena is only lit by flame and flowing lava. In the background sits an ornate building with a small brick bridge that leads to the right of the stage; the building extends offscreen into the distance. In the far back can be seen lava flowing off the cliffs within the cave. After a certain amount of time, a building will rise from the background - it is complex with numerous tubes and flaming exhausts in its lower half, but its upper half has windows and resembles a house. When this building is present, its flames will make the stage, illuminating the area with a red tint.