{"paper":{"title":"On the Enlargement by Pr\\\"ufer Objects of the Cluster Category of type $A_\\infty$","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.RT","authors_text":"Thomas A. Fisher","submitted_at":"2014-11-18T14:54:30Z","abstract_excerpt":"In a paper by Holm and Jorgensen, the cluster category $\\mathscr{D}$ of type $A_\\infty$, with Auslander-Reiten quiver $\\mathbb{Z} A_\\infty$, is introduced. Slices in the Auslander-Reiten quiver of $\\mathscr{D}$ give rise to direct systems; the homotopy colimit of such direct systems can be computed and these \"Pr\\\"ufer objects\" can be adjoined to form a larger category. It is this larger category, $\\overline{\\mathscr{D}},$ which is the main object of study in this paper. We show that $\\overline{\\mathscr{D}}$ inherits a nice geometrical structure from $\\mathscr{D}$; \"arcs\" between non-neighbouri"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1411.4856","kind":"arxiv","version":3},"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"}