So... is Caligula finished or not?
NO, it is not finished.
Why?
MangaUpdates contains information about the anime adaptation and indicates that it is incomplete.
Watching Order (by release date)
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Synopsis
Ritsu Shikishima's seemingly normal high school life is disrupted by a mysterious voice and unsettling changes to his reality.
He discovers that he's trapped in Mobius, a virtual world created by the popular idol μ.
μ's singing is turning people into monstrous Digiheads, and Ritsu must gather others who have awakened to the truth.
They gain special powers called the Catharsis Effect and must fight against the Ostinato Musicians to escape Mobius and find their way back to reality.