{"paper":{"title":"How to construct a Hovey triple from two cotorsion pairs","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AT","authors_text":"James Gillespie","submitted_at":"2014-06-10T16:28:10Z","abstract_excerpt":"Let $\\mathcal{A}$ be an abelian category, or more generally a weakly idempotent complete exact category, and suppose we have two complete hereditary cotorsion pairs $(\\mathcal{Q}, \\widetilde{\\mathcal{R}})$ and $(\\widetilde{\\mathcal{Q}}, \\mathcal{R})$ in $\\mathcal{A}$ satisfying $\\widetilde{\\mathcal{R}} \\subseteq \\mathcal{R}$ and $\\mathcal{Q} \\cap \\widetilde{\\mathcal{R}} = \\widetilde{\\mathcal{Q}} \\cap \\mathcal{R}$. We show how to construct a (necessarily unique) abelian model structure on $\\mathcal{A}$ with $\\mathcal{Q}$ (respectively $\\widetilde{\\mathcal{Q}}$) as the class of cofibrant (resp. "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1406.2619","kind":"arxiv","version":1},"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"}