The (co)homology of algebras over operads

The cohomology H∗P (A,E) of an algebra A over an operad P with coefficients in a representation E is defined by the homology of the derived functor of derivations B → DerP(B,E) on the homotopy category of P-algebras over A. There is also a homology theory HP ∗ (A,E) defined by the homology of the derived functor of B → E?UP(B)O1 P (B), where UP(B) refers to the enveloping algebra of B, the coefficient E is a right UP(A)-module, and O1 P (B) is the module of Kähler differentials of B. The first purpose of this chapter, carried out in §13.1, is to survey the definition of these derived functors for algebras and operads in dg-modules.