{"paper":{"title":"Eckmann-Hilton arguments in equivariant higher algebra","license":"http://creativecommons.org/licenses/by-nc-sa/4.0/","headline":"","cross_cats":["math.AT"],"primary_cat":"math.CT","authors_text":"Natalie Stewart","submitted_at":"2025-08-07T16:37:59Z","abstract_excerpt":"Let $\\mathcal{O}^{\\otimes}$ and $\\mathcal{P}^{\\otimes}$ be $k$- and $\\ell$-connected unital $G$-operads subject to the condition for all $S$ that $\\mathcal{O}(S) = \\emptyset$ if and only if $\\mathcal{P}(S) = \\emptyset$. We show that the Boardman-Vogt tensor product $\\mathcal{O}^{\\otimes} \\otimes \\mathcal{P}^{\\otimes}$ is $(k + \\ell + 2)$-connected; equivalently, $\\mathcal{O} \\otimes \\mathcal{P}$-monoids in any $(k + \\ell + 3)$-category lift uniquely to incomplete semi-Mackey functors. As a consequence, we show that the smashing localizations on unital $G$-operads correspond precisely to unital"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2508.05556","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2508.05556/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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"}