  In the theory of operads we consider functors of generalized symmetric powers
defined by sums of coinvariant modules under actions of symmetric groups. One
observes classically that the construction of symmetric functors provides an
isomorphism from the category of symmetric modules to a subcategory of the
category of functors on the base category. The purpose of this book is to
obtain a similar relationship for functors on a category of algebras over an
operad.
  We observe that right modules over operads, symmetric modules equipped with a
right operad action, give rise to functors on categories of algebras and we
prove that this construction yields an embedding of categories. Then we check
that right modules over operads form a model category. In addition we prove
that weak-equivalences of right modules correspond to pointwise
weak-equivalences at the functor level. As a conclusion, we obtain that right
modules over operads supply good models for the homotopy of associated functors
on algebras over operads.
