  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.
