All Questions

This a alternative form of the question I posted some time ago. We, the people who don't know topology, are told that in characteristic p the formalizm of DG algebras is not quite adequate for ...

Is there an already studied notion of $\infty$-morphism between algebras over a quasi-free operad $P = (T(E), \partial)$? If the operad $P$ is Koszul, or of the form $\Omega C$ for $C$ a cooperad, ...