A rationally inattentive screener evaluates a heterogeneous pool of candidates, aiming to let only high-productivity candidates pass. Candidates belong to distinct and observable social categories. There is heterogenity across categories along multiple dimensions, including the costs of investment in skills, the costs of being screened, and the degree of bias faced in the screening process. Candidates choose how much effort to invest in skill development before being screened, with a payoff in a post-screening market that depends on the screening outcome. We characterize equilibrium behavior in this model, and use it to unify and extend several strands in the literature on categorical inequality, including statistical discrimination, prejudice, and social capital.