In the first answer for this [question](https://mathoverflow.net/questions/5538/why-drinfeld-jimbo-type-quantum-groups) is writen, about the braided category of representation of the enveloping algebra $U(\frak{g})$, for $\frak{g}$ a semisimple Lie algebra: 

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> The space of deformations of the braided tensor structure on these particular categories is one dimensional (I believe this is a result of Drinfeld), so we get a universal family of braided deformations of U(g)-mod by varying q in U\_q(g). 
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What is the precise reference for this result? I guess here by tensor, the answerer means equivalently monoidal?

What happend if we take out "braided"? Does there exist deformations of the monoidal category of $U(\frak{g})$-modules which are not equivalent to the cateogry of modules of $U\_q(\frak{g})$, for some $q$?