Model categories 7 — Let A be a cofibrant operad as above.

Let A be a cofibrant operad as above. Use the above results to construct spectral sequences that converge to the homotopy groups of the space of A-algebra structures on a given object X, and to the homotopy groups of the mapping space of A-algebra maps between two given A-algebras. These spectral sequences for the A-infinity operad are the key formal ingredients to the Hopkins-Miller proof that Morava E-theory admits an action by the stabilizer group.