Document type
ArticleVersion
Accepted versionPublication date
Publication license
Please use this identifier to cite or link to this item: https://hdl.handle.net/2445/184903
Comparing localizations across adjunctions
Journal Title
Director/Tutor
Journal ISSN
Volume Title
Related resource
Abstract
We show that several apparently unrelated formulas involving left or right Bousfield localizations in homotopy theory are induced by comparison maps associated with pairs of adjoint functors. Such comparison maps are used in the article to discuss the existence of functorial liftings of homotopical localizations and cellularizations to categories of algebras over monads acting on model categories, with emphasis on the cases of module spectra and algebras over simplicial operads. Some of our results hold for algebras up to homotopy as well; for example, if $T$ is the reduced monad associated with a simplicial operad and $f$ is any map of pointed simplicial sets, then $f$-localization coincides with $T f$-localization on spaces underlying homotopy $T$-algebras, and similarly for cellularizations.
Subject (English)
Citation
Citation
CASACUBERTA, Carles, RAVENTÓS MORERA, Oriol and TONKS, Andrew. Comparing localizations across adjunctions. Transactions of the American Mathematical Society. 2021. Vol. 374, num. 11, pags. 7811-7865. ISSN 0002-9947. [consulted: 15 of June of 2026]. Available at: https://hdl.handle.net/2445/184903