The monadic tower for ∞-categories

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Abstract

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
Volume226
Issue number6
DOIs
StatePublished - Jun 2022
Externally publishedYes

Bibliographical note

Publisher Copyright:
© 2021 Elsevier B.V.

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