I will discuss joint work with Terry Gannon in which we provide a ribbon tensor equivalence between the representation category of small quantum SL(2), at parameter q=exp(pi i/p), and the representation category of the triplet vertex operator algebra at integral parameter p>1. We provide similar quantum group equivalences for representation categories associated to the Virasoro, and singlet vertex operator algebras at central charge c=1-6(p-1)^2/p.