Monadicity of the Bousfield–Kuhn functor

Rosona Eldred; Gijs Heuts; Akhil Mathew; Lennart Meier

doi:10.1090/proc/14331

Monadicity of the Bousfield–Kuhn functor

Rosona Eldred
, Gijs Heuts
, Akhil Mathew
, Lennart Meier

Research output: Contribution to journal › Article › Academic › peer-review

Abstract

Let M _n ^f be the localization of the ∞-category of spaces at the v _n -periodic equivalences, the case n = 0 being rational homotopy theory. We prove that M _n ^f is for n ≥ 1 equivalent to algebras over a certain monad on the ∞-category of T (n)-local spectra. This monad is built from the Bousfield– Kuhn functor.

Original language	English
Pages (from-to)	1789-1796
Number of pages	8
Journal	Proceedings of the American Mathematical Society
Volume	147
Issue number	4
DOIs	https://doi.org/10.1090/proc/14331
Publication status	Published - 8 Jan 2019

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AU - Heuts, Gijs

AU - Mathew, Akhil

AU - Meier, Lennart

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AB - Let M n f be the localization of the ∞-category of spaces at the v n -periodic equivalences, the case n = 0 being rational homotopy theory. We prove that M n f is for n ≥ 1 equivalent to algebras over a certain monad on the ∞-category of T (n)-local spectra. This monad is built from the Bousfield– Kuhn functor.

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Monadicity of the Bousfield–Kuhn functor

Abstract

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