{"paper":{"title":"On homological finiteness properties and free inverse monoids","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.RA"],"primary_cat":"math.GR","authors_text":"Carl-Fredrik Nyberg-Brodda","submitted_at":"2026-06-29T15:11:56Z","abstract_excerpt":"We construct a simple and useful sufficient condition, based on actions on a lattice of idempotents, for monoids admitting homomorphisms to the monogenic free inverse monoid $\\mathrm{FIM}(1)$ to not be of type $\\mathrm{FP}_2$. This recovers a result of Gray and Steinberg that free inverse monoids are not of type $\\mathrm{FP}_2$. The same technique is then used to show that a finitely generated submonoid of $\\mathrm{FIM}(1)$ is of type $\\mathrm{FP}_2$ if and only if it is finitely presented, answering a question of Cho & Ru\\v{s}kuc."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2606.30434","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2606.30434/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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"}