{"paper":{"title":"On reachability categories, persistence, and commuting algebras of quivers","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["math.CO","math.CT"],"primary_cat":"math.RA","authors_text":"Henri Riihim\\\"aki, Luigi Caputi","submitted_at":"2023-06-27T11:26:47Z","abstract_excerpt":"For a finite quiver $Q$, we study the reachability category $\\mathbf{Reach}_Q$. We investigate the properties of $\\mathbf{Reach}_Q$ from both a categorical and a topological viewpoint. In particular, we compare $\\mathbf{Reach}_Q$ with $\\mathbf{Path}_Q$, the category freely generated by $Q$. As a first application, we study the category algebra of $\\mathbf{Reach}_Q$, which is isomorphic to the commuting algebra of $Q$. As a consequence, we recover, in a categorical framework, previous results obtained by Green and Schroll; we show that the commuting algebra of $Q$ is Morita equivalent to the in"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2306.15388","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2306.15388/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"}