The Library is a fighting arena in Sonic Battle. It is treated as Cream's home arena.
The Library is located within the government building (called the Central Lab), and is designed like some kind of natural history museum as the center of the arena has a large dinosaur skeleton embedded in the floor. It is perhaps the smallest arena in the game, and with the walls being on the sides of the arena, there are few hiding places, encouraging all-out fighting.
This arena has little presence in the story, as it is primarily used for when Tails attempts to use the Library to access data on Emerl, only to breach government confidentiality and be attacked by Guard Robos. Later, in Emerl's story, Emerl can train with Cream here.