The Monadic Tower for $\infty$-Categories

Abstract

Every right adjoint functor between presentable $\infty$-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.

arXiv comment25 pages. Moved example 4.1 to the introduction, replaced remark 2.15 with a more detailed discussion and made minor corrections. Final version to appear in JPAA

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