{"paper":{"title":"Quillen equivalences for stable categories","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AC","math.AT","math.RT"],"primary_cat":"math.CT","authors_text":"Georgios Dalezios, Henrik Holm, Sergio Estrada","submitted_at":"2016-10-05T17:59:26Z","abstract_excerpt":"For an abelian category $\\mathcal{A}$ we investigate when the stable categories $\\underline{\\mathrm{GPro}}\\mathrm{j}(\\mathcal{A})$ and $\\underline{\\mathrm{GIn}}\\mathrm{j}(\\mathcal{A})$ are triangulated equivalent. To this end, we realize these stable categories as homotopy categories of certain (non-trivial) model categories and give conditions on $\\mathcal{A}$ that ensure the existence of a Quillen equivalence between the model categories in question. We also study when such a Quillen equivalence transfers from $\\mathcal{A}$ to categories naturally associated to $\\mathcal{A}$, such as $\\mathr"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1610.02073","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"}