Well, it's not entirely a parody. But there are absolutely parodic incidents. It takes the name Ulysses to allude to a grand epic, and then focuses on three people living a day in their lives. And it's not a parody in the sense that Joyce is making a bigger point, which is that the human mind is so complex and beautiful that the mere fact of living a day is an epic unto itself.

However, Joyce still absolutely has a comedic mindset. The opening, when Buck Mulligan descends and shaves, is written as if it were a religious ritual. There's the excellent newspaper scene, where headlines announce the goings-on of the characters. There's a chapter where every few paragraphs Joyce takes on the style of a new writer, moving from extremely obtuse ancient writing up to Irish slang. There's the penultimate chapter, which takes a scientific approach to two characters having sex. Stephen's chapter is a parody of the overthinking genius. Really, every chapter is as silly as it's straight. It's one of the things that makes Ulysses so fascinating.

Technically, I'd call Finnegans Wake an even greater parody, but that's not fair, because it parodies itself.