In the inferno, dante uses
to associate himself with classical writers and thinkers.

The answer is Comedy.

Inferno is a book written by Dante Alighieri telling us his journey to hell. It contains Introduction or Overview and Chapters of 9 Circles of Hell. This is based on comedy genre.

The Nine Circles of Hell are the following:

Limbo - Wherein pagans are being punished. Some of the people he has seen there are: Virgil, Homer, Horace, Plato and Socrates.Lust - Wherein souls are suffering and being torn in strong wind. He has seen the following souls in there: Francesca de Rimini and her lover.Gluttony - Souls are lying down in freezing slush and being watched over by Cerberus, a dog with 3 heads. Avarice and Prodigality - Souls are crushed through heavy weights objects over and over again.Wrath - Souls who are wrathful are being punished by making them fight one another.Heresy - Souls are being punished by getting cooked in flames. Violence - Violent souls are being punished by getting eaten by Minotaur repeatedly. Fraud - seducers, false prophets, liars and thieves are being punished by different methods, depending on their sins.Treachery - sinners are being punished by freezing them in the frozen lake. Satan  is there together with Judas, Brutus and Cassius.