The comic book issue Back to the Future 3 is an adaptation of this episode.
In the question and answer session at USC, Robert Zemeckis and Bob Gale discussed their view of time travel. "You travel through time, you don't travel through space," Zemeckis noted, "and most of your time travel movies make that fatal mistake. You're in California, and you travel back to ancient Rome. How did you get to Rome, if you're in this longitude and latitude?" In this episode of the animated series, of course, the DeLorean indeed does travel from California to ancient Rome. It should be noted, of course, that in order to sustain a weekly series, particularly for a cartoon, the characters would need to travel to other locations besides California.
With Marty as company, Doc heads to Ancient Rome to return overdue library books. Jules and Verne overhear their father talk about the arcades and stow away in the DeLorean to play the Roman "video games, (the boys have been forbidden to leave the house because they mis-use their father's latest invention - a holographic device.) Once there, Marty insults Bifficus and is challenged to a chariot race. Doc is mistaken for a rebellious slave and is going to be thrown to the lions. The boys run amok in Ancient Rome and end up meeting Judah, a slave, who helps them get out of trouble. In the end, Marty loses the race because Bifficus must rise to power in order for the Roman Empire to fall. Doc uses his holographic device to avoid becoming lion chow and the boys help Judah escape to become a free man.