The monadic tower for ∞-categories

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Every right adjoint functor between presentable ∞-categories is shown to decompose canonically as a coreflection, followed by, possibly transfinitely many, monadic functors. Furthermore, the coreflection part is given a presentation in terms of a functorial iterated colimit. Background material, examples, and the relation to homology localization and completion are discussed as well.[Formula presented] Weltchronik in Versen, Szene: Der Turmbau zu Babel (c. 1370s). Depiction of the construction of the tower of Babel.

Original languageAmerican English
Article number106975
JournalJournal of Pure and Applied Algebra
Issue number6
StatePublished - Jun 2022
Externally publishedYes

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