{"paper":{"title":"Gcd-monoids arising from homotopy groupoids","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.GR","authors_text":"Friedrich Wehrung (LMNO)","submitted_at":"2017-12-07T09:26:21Z","abstract_excerpt":"The interval monoid $\\Upsilon$(P) of a poset P is defined by generators [x, y], where x $\\le$ y in P , and relations [x, x] = 1, [x, z] = [x, y] $\\times$ [y, z] for x $\\le$ y $\\le$ z. It embeds into its universal group $\\Upsilon$ $\\pm$ (P), the interval group of P , which is also the universal group of the homotopy groupoid of the chain complex of P. We prove the following results: $\\bullet$ The monoid $\\Upsilon$(P) has finite left and right greatest common divisors of pairs (we say that it is a gcd-monoid) iff every principal ideal (resp., filter) of P is a join-semilattice (resp., a meet-sem"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1712.02787","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"}