To find a universal way of  quantizing Lie bialgebras has been a problem posed by Drinfel’d and its solution has been provided by Etingof and Kazhdan. It is hard to overstimate the importance of their results for the theory of quantum groups and also seemingly unrelated research areas. After their result, Ševera proposed a rather simple way to obtain the same result. The aim of this talk is to explain that one can use a mixture of both results to get a full picture of the quantization of (co)Poisson Hopf algebras, and moreover, to construct an inverse functor, called dequantization, along the same lines. If time permits, I will explain how our result can be used to construct a Gerstenhaber up to homotopy structure on the Hochschild cochains of an associative algebra.

This is based on a joint work with Andrea Rivezzi (https://arxiv.org/abs/2602.03810).