The Monadic Tower for $\infty$-Categories
Algebraic Topology
2021-11-23 v3 Category Theory
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.
Cite
@article{arxiv.2104.01816,
title = {The Monadic Tower for $\infty$-Categories},
author = {Lior Yanovski},
journal= {arXiv preprint arXiv:2104.01816},
year = {2021}
}
Comments
25 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