Following Beilinson and Drinfeld, we describe vertex algebras as Lie algebras in a certain pseudo-tensor category. More
precisely, starting from a vector superspace V with a linear operator on it, we introduce the operad of n-ary chiral operations on V. When V is equipped with a vertex algebra structure, this allows us to define the cohomology of V with coefficients in a V-module. We introduce a filtration on the chiral operad and describe its associated graded operad in terms of acyclic graphs. We show that a Lie algebra for the latter operad is the same as a Poisson vertex algebra. This is a joint work with Alberto De Sole, Reimundo Heluani, and Victor Kac.