{"paper":{"title":"Simplicial geometry of unital lattice-ordered abelian groups","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.LO"],"primary_cat":"math.CO","authors_text":"Leonardo Manuel Cabrer","submitted_at":"2012-02-21T18:08:37Z","abstract_excerpt":"By an $\\ell$-group $G$ we mean a lattice-ordered abelian group. This paper is concerned with the category $\\FP$ of finitely presented {\\it unital} $\\ell$-groups, those $\\ell$-groups having a distinguished order-unit $u$. Using the duality between $\\FP$ the category of rational polyhedra, we will provide (i) a construction of finite limits and co-limits in $\\FP$; (ii) a Cantor-Bernstein-Schr\\\"oder theorem for finitely presented unital $\\ell$-groups; (iii) a geometrical characterization of finitely generated subalgebras of free objects of $\\FP$."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1202.5947","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"}