Homology, Homotopy and Applications

Volume 23 (2021)

Number 2

Left Bousfield localization and Eilenberg–Moore categories

Pages: 299 – 323

DOI: https://dx.doi.org/10.4310/HHA.2021.v23.n2.a16


Michael Batanin (Mathematical Institute of the Academy, Prague, Czech Republic)

David White (Department of Mathematics and Computer Science, Denison University, Granville, Ohio, U.S.A.)


We prove the equivalence of several hypotheses that have appeared recently in the literature for studying left Bousfield localization and algebras over a monad. We find conditions so that there is a model structure for local algebras, so that localization preserves algebras, and so that localization lifts to the level of algebras. We include examples coming from the theory of colored operads, and applications to spaces, spectra, and chain complexes.


monads, homotopy theory of algebras, left Bousfield localisation

2010 Mathematics Subject Classification

18C20, 18G55, 55P48, 55P60, 55U35

Copyright © 2021, Michael Batanin and David White. Permission to copy for private use granted.

The second author was supported by the National Science Foundation under Grant No. IIA-1414942.

Received 14 May 2018

Received revised 4 January 2021

Accepted 5 January 2021

Published 18 August 2021