English

Right Bousfield Localization and Operadic Algebras

Algebraic Topology 2021-09-14 v2 Category Theory K-Theory and Homology Rings and Algebras Representation Theory

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

R2 v1 2026-06-22T12:16:57.527Z