  We introduce the notion of homotopy inner products for any cyclic quadratic
Koszul operad $\mathcal O$, generalizing the construction already known for the
associative operad. This is done by defining a colored operad $\hat{\mathcal
O}$, which describes modules over $\mathcal O$ with invariant inner products.
We show that $\hat{\mathcal O}$ satisfies Koszulness and identify algebras over
a resolution of $\hat{\mathcal O}$ in terms of derivations and module maps. An
application to Poincar\'e duality on the chain level of a suitable topological
space is given.
