The transversity distribution was recently extracted from deep-inelastic scattering processes producing hadron pairs in the final state. Together with a specific chiral-odd di-hadron fragmentation function, it is involved in the elementary mechanism that generates a transverse-spin asymmetry in the azimuthal distribution of the detected hadron pairs. The same elementary mechanism was predicted to generate an analogous asymmetry when the hadron pairs are produced in proton-proton collisions with one transversely polarized proton. Recently, the STAR Collaboration has observed this asymmetry. We analyze the impact of these data on our knowledge of transversity.