  In this paper we develop the theory of operads, algebras and modules in
cofibrantly generated symmetric monoidal model categories. We give J-semi model
strucures, which are a slightly weaker version of model structures, for operads
and algebras and model structures for modules. In a second part we develop the
thoery of S-modules of [EKMM]., which allows a general homotopy theory for
commutative algebras and pseudo unital symmetric monoidal categories of modules
over them. Finally we prove a base change and projection formula.

Algebraic Topology;Category Theory