I will try to show how how the Rozansky-Witten topological quantum field based on a complex symplectic manifold leads to thinking of the derived category of a complex manifold as the representation category of a Lie algebra object, or of a certain associative algebra object (the universal enveloping algebra) which behaves a lot like a finite group algebra. This gives another way of thinking of the Hochschild (co)homology of a complex manifold.