{"paper":{"title":"The $\\infty$-Categorical Eckmann-Hilton Argument","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AT","authors_text":"Lior Yanovski, Tomer Schlank","submitted_at":"2018-08-17T21:40:04Z","abstract_excerpt":"We define a reduced $\\infty$-operad $\\mathcal{P}$ to be $d$-connected if the spaces $\\mathcal{P}\\left(n\\right)$, of $n$-ary operations, are $d$-connected for all $n\\ge0$. Let $\\mathcal{P}$ and $\\mathcal{Q}$ be two reduced $\\infty$-operads. We prove that if $\\mathcal{P}$ is $d_{1}$-connected and $\\mathcal{Q}$ is $d_{2}$-connected, then their Boardman-Vogt tensor product $\\mathcal{P}\\otimes\\mathcal{Q}$ is $\\left(d_{1}+d_{2}+2\\right)$-connected. We consider this to be a natural $\\infty$-categorical generalization of the classical Eckmann-Hilton argument."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1808.06006","kind":"arxiv","version":3},"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/1808.06006/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"}