Latin quarter hat
Mulligan tosses Stephen his "Latin quarter hat" as the young men prepare to begin their day outside the tower, and in Proteus Stephen, reminiscing about his time in Paris, thinks of the counter-cultural poses that both he and Mulligan are striking in the world: "My Latin quarter hat. God, we simply must dress the character." (Haines too dresses informally in a "soft grey hat.")
Gifford describes Stephen's hat as “A soft or slouch hat associated with the art and student worlds of the Latin Quarter in Paris, as against the 'hard' hats (bowlers or derbies) then fashionable in Dublin.” In December 1902 Joyce mailed a Parisian photo-postcard of himself posing in such a hat to his friend J. F. Byrne. The look contrasts sharply with most of the headgear that one would have seen on Dublin streets.
In Proteus Stephen thinks of this bohemian topper as "my Hamlet hat." But its resemblance to certain clerical chapeaux causes some people to refer to Stephen as a clergyman. Early in Oxen of the Sun he is described as having the "mien of a frere," and near the end of the chapter someone says or thinks, “Jay, look at the drunken minister coming out of the maternity hospal! Benedicat vos omnipotens Deus, Pater et Filius.” Shortly later, he is called "Parson Steve." At the beginning of the next chapter, Circe, two British soldiers call out derisively to him as "parson."