In the PS2 update, Persona 3: FES, in the chapter "The Answer", all levels of the Abyss of Time get their names from Dante's "The Divine Comedy":
• The First Door, Malebolge, is the level where people who commit fraud are punished.
• The Second Door, Cocytus, is the lowest level of hell divided into for regions (the next four) where people who commit the sin of betrayal are punished.
• The Third Door, Caina, named after the Bible's Cain, is where people who betrayed family dwell.
• The Fourth Door, Antenora, named after Antenor from Homer's "The Iliad", is where people who betrayed their country dwell.
• The Fifth Door, Ptolomea, named after Ptolemy, governor of Jericho from the Bible who killed his guests, is where people who betrayed guests dwell.
• The Sixth Door, Judecca, named after Judas Iscariot also from the Bible, is where people who betray masters or benefactors dwell.
• The Seventh Door, Empyrean, is named after the the highest level of Heaven.