Poincar\'e/Koszul duality

We prove a duality for factorization homology which generalizes both usual Poincar'e duality for manifolds and Koszul duality for ${\mathcal{E}}_n$-algebras. The duality has application to the Hochschild homology of associative algebras and enveloping algebras of Lie algebras. We interpret our result at the level of topological quantum field theory.