Right Bousfield Localization and Operadic Algebras
Abstract
It is well known that under some general conditions right Bousfield localization exists. We provide general conditions under which right Bousfield localization yields a monoidal model category. Then we address the questions of when this monoidal model structure on a right Bousfield localization induces a model structure on the category of algebras over a colored operad and when a right Bousfield localization preserves colored operadic algebras. We give numerous applications, to topological spaces, equivariant spaces, chain complexes, stable module categories, and to the category of small categories. We recover a wide range of classical results as special cases of our theory, and prove several new preservation results.
Keywords
Cite
@article{arxiv.1512.07570,
title = {Right Bousfield Localization and Operadic Algebras},
author = {David White and Donald Yau},
journal= {arXiv preprint arXiv:1512.07570},
year = {2021}
}
Comments
version 2 adds new results proving that algebras over operads in G spaces and G spectra admit transferred model structures. There are also new algebraic examples. Edits made in response to a referee