Monadicity of the Bousfield-Kuhn functor

Rosona Eldred; Gijs Heuts; Akhil Mathew; Lennart Meier

Monadicity of the Bousfield-Kuhn functor

Algebraic Topology 2017-07-20 v1

Authors: Rosona Eldred , Gijs Heuts , Akhil Mathew , Lennart Meier

Abstract

We consider the localization of the $\infty$ -category of spaces at the $v_n$ -periodic equivalences, the case $n=0$ being rational homotopy theory. We prove that this localization is for $n\geq 1$ equivalent to algebras over a certain monad on the $\infty$ -category of $T(n)$ -local spectra. This monad is built from the Bousfield--Kuhn functor.

Keywords

Bousfield-Kuhn functor monadicity infinity-category localization v_n-periodic equivalences T(n)-local spectra rational homotopy theory

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@article{arxiv.1707.05986,
  title  = {Monadicity of the Bousfield-Kuhn functor},
  author = {Rosona Eldred and Gijs Heuts and Akhil Mathew and Lennart Meier},
  journal= {arXiv preprint arXiv:1707.05986},
  year   = {2017}
}

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8 pages

Monadicity of the Bousfield-Kuhn functor

Abstract

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