In this joint work with Pavol Ševera, we describe a simple way to quantize commutative Hopf algebras with compatible Poisson brackets, of which Lie bialgebras give an important example. Nerves of such Hopf algebras can be seen as braided lax monoidal functors from the PROP governing commutative algebras with an infinitesimal braiding. Precomposing with a Drinfeld associator, we get a functor from the PROP of braided commutative algebras. This functor is then the nerve of a Hopf algebra quantizing the original Poisson bracket.