{"paper":{"title":"Model structure on projective systems of $C^*$-algebras and bivariant homology theories","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AT","math.OA"],"primary_cat":"math.KT","authors_text":"Ilan Barnea, Michael Joachim, Snigdhayan Mahanta","submitted_at":"2015-08-18T11:36:41Z","abstract_excerpt":"Using the machinery of weak fibration categories due to Schlank and the first author, we construct a convenient model structure on the pro-category of separable $C^*$-algebras $\\mathrm{Pro}(\\mathtt{SC^*})$. The opposite of this model category models the $\\infty$-category of pointed noncommutative spaces $\\mathtt{N}\\mathcal{S_*}$ defined by the third author. Our model structure on $\\mathrm{Pro}(\\mathtt{SC^*})$ extends the well-known category of fibrant objects structure on $\\mathtt{SC^*}$. We show that the pro-category $\\mathrm{Pro}(\\mathtt{SC^*})$ also contains, as a full coreflective subcateg"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1508.04283","kind":"arxiv","version":2},"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"}