## Monadicity of the Bousfield–Kuhn functor

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- by Rosona Eldred, Gijs Heuts, Akhil Mathew and Lennart Meier
- Proc. Amer. Math. Soc.
**147**(2019), 1789-1796 - DOI: https://doi.org/10.1090/proc/14331
- Published electronically: January 8, 2019
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## Abstract:

Let $\mathscr {M}_n^f$ be 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 $\mathscr {M}_n^f$ 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.## References

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## Bibliographic Information

**Rosona Eldred**- Affiliation: Max-Planck-Institut, Vivatsgasse 7, 53111 Bonn, Germany
- MR Author ID: 1015629
**Gijs Heuts**- Affiliation: Mathematical Institute, Utrecht University, 3584CD Utrecht, The Netherlands
- MR Author ID: 1082480
**Akhil Mathew**- Affiliation: Department of Mathematics, University of Chicago, Chicago, Illinois 60637-1514
- MR Author ID: 891016
**Lennart Meier**- Affiliation: Mathematical Institute, Utrecht University, 3584CD Utrecht, The Netherlands
- MR Author ID: 955940
- Received by editor(s): March 29, 2018
- Received by editor(s) in revised form: July 10, 2018
- Published electronically: January 8, 2019
- Additional Notes: This work was begun through a Junior Trimester Program at the Hausdorff Institute of Mathematics, and we thank the HIM for its hospitality.

The second author was supported by the European Research Council (ERC) under the European Union’s Horizon 2020 research and innovation programme (grant agreement no. 682922).

The third author was supported by the NSF Graduate Fellowship under grant DGE-114415 and was a Clay Research Fellow when this work was finished.

The fourth author was supported by DFG SPP 1786. - Communicated by: Mark Behrens
- © Copyright 2019 American Mathematical Society
- Journal: Proc. Amer. Math. Soc.
**147**(2019), 1789-1796 - MSC (2010): Primary 55Q51
- DOI: https://doi.org/10.1090/proc/14331
- MathSciNet review: 3910443