{"paper":{"title":"Monadicity of the Bousfield-Kuhn functor","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AT","authors_text":"Akhil Mathew, Gijs Heuts, Lennart Meier, Rosona Eldred","submitted_at":"2017-07-19T09:04:31Z","abstract_excerpt":"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."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1707.05986","kind":"arxiv","version":1},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"}