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 $Tf$-localization on spaces underlying homotopy $T$-algebras, and similarly for cellularizations.

---

中文翻译：

---

比较不同附件的本地化

摘要：我们表明，同伦理论中涉及左或右 Bousfield 定位的几个明显不相关的公式是由与伴随函子对相关的比较映射引起的。文章中使用此类比较图来讨论同伦定位和细胞化对代数类别的泛函提升的存在，这些类别对作用于模型类别的 monad 而言，重点是模块谱和代数对单纯操作数的情况。我们的一些结果也适用于同伦的代数；例如，如果 $T$ 是与单纯操作数相关联的约化 monad，而 $f$ 是指向单纯集的任何映射，则 $f$-localization 与 $Tf$-localization 在同伦 $T$-algebras 基础上的空间一致，以及类似的细胞化。

---