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arXiv · 2104.01816

The Monadic Tower for $\infty$-Categories

Lior Yanovski
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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.

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Lior Yanovski. 2021-04-05. The Monadic Tower for $\infty$-Categories. https://arxiv.org/abs/2104.01816

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