Mulligan emerges from the stairhead with the tools of his morning shaving ritual: a "bowl of lather on which a mirror and a razor lay crossed." The fact that the mirror and razor lie "crossed" obliquely announces that Mulligan will soon be parodying a Catholic priest celebrating Mass. But these two objects also obliquely signal the tensions in the relationship between Mulligan and Stephen Dedalus—tensions that emerge in very concrete physical forms like the experience of seeing oneself as an object (the mirror) and the threat of bodily harm (the razor).
Later in the chapter, Mulligan will thrust the mirror in Stephen's face: "Look at yourself, he said, you dreadful bard!" Stephen sees a poorly dressed, lice-infested body and thinks of a Robert Burns poem about the humbling effect of beholding oneself objectively, as others do. Mulligan has his own unflattering literary analogue for Stephen staring into the glass; he thinks of Oscar Wilde's sentences about the ugly and bestial Caliban seeing his face in a mirror. Stephen steps back from the mirror, and from these bitter self-reflections, to make the glass emblematic of the literary art that he hopes to practice: "It is a symbol of Irish art. The cracked lookingglass of a servant." For Joyce, fiction had the duty to represent human reality accurately, and that meant depicting Irish society with all its paralyzing flaws. The first person to whom Ulysses holds up a mirror is Oliver St. John Gogarty, a.k.a. Mulligan.
The razor too accretes associations as the chapter goes on. Mulligan repeatedly calls Stephen “Kinch” and explains the significance of his nickname: "O, my name for you is the best: Kinch, the knife-blade." But knives are not associated only with the perverse jesuit who "killed his mother" and has "something sinister" in him. They also adhere to the man who shaves his face on top of the tower, and who "lunges" toward each of his companions in the room below "a thick slice of bread, impaled on his knife." Mulligan is a medical student, and has seen corpses "cut up into tripes in the dissectingroom." As Antinous and Claudius in the Homeric and Shakespearean analogues underlying the tower ménage, he carries concealed weapons, looking for opportunities to do harm.
All of these associations resonate as Mulligan hooks "his arm in Stephen's and walk[s] with him round the tower, his razor and mirror clacking in the pocket where he had thrust them," and as Stephen contemplates the exchange about mirrors that precedes the seemingly friendly linking of arms: "Parried again. He fears the lancet of my art as I fear that of his. The cold steelpen.” The two men are locked in an embrace that is anything but genial. In symbols like mirrors and razors, and in actual physiological phenomena like flushed cheeks, their bodies tell the story of rising hatred.