{"paper":{"title":"Symmetric monoidal noncommutative spectra, strongly self-absorbing $C^*$-algebras, and bivariant homology","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AT","math.OA"],"primary_cat":"math.KT","authors_text":"Snigdhayan Mahanta","submitted_at":"2014-03-17T15:34:12Z","abstract_excerpt":"Continuing our project on noncommutative (stable) homotopy we construct symmetric monoidal $\\infty$-categorical models for separable $C^*$-algebras $\\mathtt{SC^*_\\infty}$ and noncommutative spectra $\\mathtt{NSp}$ using the framework of Higher Algebra due to Lurie. We study smashing (co)localizations of $\\mathtt{SC^*_\\infty}$ and $\\mathtt{NSp}$ with respect to strongly self-absorbing $C^*$-algebras. We analyse the homotopy categories of the localizations of $\\mathtt{SC^*_\\infty}$ and give universal characterizations thereof. We construct a stable $\\infty$-categorical model for bivariant connect"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1403.4130","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":""},"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"}