{"paper":{"title":"Colocalizations of noncommutative spectra and bootstrap categories","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":"2014-12-29T15:17:01Z","abstract_excerpt":"We construct a compactly generated and closed symmetric monoidal stable $\\infty$-category $\\mathtt{NSp'}$ and show that $\\mathtt{hNSp'}^{op}$ contains the suspension stable homotopy category of separable $C^*$-algebras $\\mathtt{\\Sigma Ho^{C^*}}$ constructed by Cuntz-Meyer-Rosenberg as a fully faithful triangulated subcategory. Then we construct two colocalizations of $\\mathtt{NSp'}$, namely, $\\mathtt{NSp'}[\\mathbb{K}^{-1}]$ and $\\mathtt{NSp'}[\\mathcal{Z}^{-1}]$, both of which are shown to be compactly generated and closed symmetric monoidal. We prove that Kasparov $KK$-category of separable $C"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1412.8370","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"}