  It is shown that every $2$-shifted Poisson structure on a finitely generated
semi-free commutative differential graded algebra $A$ defines a very explicit
infinitesimal $2$-braiding on the homotopy $2$-category of the symmetric
monoidal dg-category of finitely generated semi-free $A$-dg-modules. This
provides a concrete realization, to first order in the deformation parameter
$\hbar$, of the abstract deformation quantization results in derived algebraic
geometry due to Calaque, Pantev, To\"en, Vaqui\'e and Vezzosi. Of particular
interest is the case when $A$ is the Chevalley-Eilenberg algebra of a higher
Lie algebra, where the braided monoidal deformations developed in this paper
may be interpreted as candidates for representation categories of `higher
quantum groups'.
