{"paper":{"title":"Applications of Balanced Pairs","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.RA"],"primary_cat":"math.RT","authors_text":"Huanhuan Li, Junfu Wang, Zhaoyong Huang","submitted_at":"2015-07-14T14:27:49Z","abstract_excerpt":"Let $(\\mathscr{X}$, $\\mathscr{Y})$ be a balanced pair in an abelian category. We first introduce the notion of cotorsion pairs relative to $(\\mathscr{X}$, $\\mathscr{Y})$, and then give some equivalent characterizations when a relative cotorsion pair is hereditary or perfect. We prove that if the $\\mathscr{X}$-resolution dimension of $\\mathscr{Y}$ (resp. $\\mathscr{Y}$-coresolution dimension of $\\mathscr{X}$) is finite, then the bounded homotopy category of $\\mathscr{Y}$ (resp. $\\mathscr{X}$) is contained in that of $\\mathscr{X}$ (resp. $\\mathscr{Y}$). As a consequence, we get that the right $\\m"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1507.03862","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"}