{"paper":{"title":"Cotorsion pairs in cluster categories of type $A_{\\infty}^{\\infty}$","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.CO"],"primary_cat":"math.RT","authors_text":"Bin Zhu, Huimin Chang, Yu Zhou","submitted_at":"2017-04-13T07:30:13Z","abstract_excerpt":"In this paper, we give a complete classification of cotorsion pairs in a cluster category $\\mathscr{C}$ of type $A^\\infty_\\infty$ via certain configurations of arcs, called $\\tau$-compact Ptolemy diagrams, in an infinite strip with marked points. As applications, we classify $t$-structures and functorially finite rigid subcategories in $\\mathscr{C}$, respectively. We also deduce Liu-Paquette's classification of cluster tilting categories of $\\mathscr{C}$ and Ng's classification of torsion pairs in the cluster category of type $A_\\infty$."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1704.04019","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"}