{"paper":{"title":"On Semisimple Proto-Abelian Categories Associated to Inverse Monoids","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":[],"primary_cat":"math.RT","authors_text":"Alexander Sistko","submitted_at":"2025-03-05T18:56:07Z","abstract_excerpt":"Let $G$ be a finite abelian group written multiplicatively, with $\\hat{G} = G\\sqcup \\{0\\}$ the pointed abelian group formed by adjoining an absorbing element $0$. There is an associated finitary, proto-abelian category $\\operatorname{Vect}_{\\hat{G}}$, whose objects can be thought of as finite-dimensional vector spaces over $\\hat{G}$. The class of $\\hat{G}$-linear monoids are then defined in terms of this category. In this paper, we study the finitary, proto-abelian category $\\operatorname{Rep}(M,\\hat{G})$ of finite-dimensional $\\hat{G}$-linear representations of a $\\hat{G}$-linear monoid $M$. "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2503.03741","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2503.03741/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"}