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Everything you need to know about Mulligan is in this brief exchange. He’s the kind of guy who steals a broken mirror from one of his aunt’s servants, and then makes fun of her for being ugly. Joyce has shown us this type before in his short story “Two Gallants,” starring Lenehan and Corley, who also appear in Ulysses.
Mulligan’s line about the “rage of Caliban” is lifted from Oscar Wilde, who in the preface to the Portrait of Dorian Gray says “The nineteenth-century dislike of realism is the rage of Caliban seeing his own face in a glass. The nineteenth-century dislike of romanticism is the rage of Caliban not seeing his own face in a glass.” It’s interesting that this follows Stephen’s interior moment (on the last page) where he doesn’t recognize his face, or rather, wonders who “chose this face for me.”
And as for Ursula… a virgin of note, a leader of virgins, probably apocryphal. Her name means a little (female) bear.