Modules over operads and functors
Abstract
Description
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.
This book project has been withdrawn from arXiv. Final version to appear as a Springer-Verlag Lecture Notes with significant additions and corrections. The preprint on arXiv will not be updated
This book project has been withdrawn from arXiv. Final version to appear as a Springer-Verlag Lecture Notes with significant additions and corrections. The preprint on arXiv will not be updated