The first time we meet Catherine, she is presented as an object of Eddie's desire, and Miller presents her to us as if from Eddie's perspective. Catherine is wearing a skirt that she has just purchased, and she asks Eddie if he likes it. In the stage directions, Miller describes her as "running her hands over her skirt." Eddie then tells her to turn around so that he can better admire how she looks in the skirt. This is Catherine's first appearance, and she comes across primarily as an object of Eddie's desire. Catherine is Eddie's niece and like a daughter to him, and his seeming desire for her in this opening scene is awkward and uncomfortable because of their relationship.
Throughout the play we also see how Eddie infantilizes Catherine. He treats her and loves her as if she is a child, and he does so in part because he wants her to be dependent upon him. Through Eddie's infantilization of her, Miller presents Catherine as an object of Eddie's jealous, possessive love. In act 1, Eddie tells Catherine, "I'm responsible for you. You're a baby." Also in act 1, Miller writes in the stage directions that Eddie has "a sense of [Catherine's] childhood, her babyhood," and Catherine says to Beatrice, speaking about Eddie, "He thinks I'm a baby." Eddie loves Catherine like a father might love a baby, because, in this way, he can convince himself that he will never lose her and that his love will remain unrivalled.