Right Bousfield localization and operadic algebras

D. White, D. Yau

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, spectra, chain complexes, stable module categories, and examples drawn from category theory. We recover a wide range of classical results as special cases of our theory, and prove several new preservation results. 

Tbilisi Mathematical Journal, Special Issue (HomotopyTheorySpectra - 2020), pp. 71-118