{"paper":{"title":"$g$-vector fans and picture categories for 0-Auslander extriangulated categories","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":[],"primary_cat":"math.RT","authors_text":"Erlend D. B{\\o}rve, Maximilian Kaipel","submitted_at":"2026-08-13T12:41:32Z","abstract_excerpt":"We extend the notion of $\\mathbf{g}$-vector fan so that it is defined for a Hom-finite Krull-Schmidt 0-Auslander $k$-linear extriangulated category $\\mathcal{C}$ with a projective silting object $T$. Moreover, we show that the $\\mathbf{g}$-vector fan admits an admissible partition, in the sense of the second-named author, which is induced by thick subcategories. One can thus define the picture category of $\\mathcal{C}$. We establish a bijection between thick subcategories of $\\mathcal{C}$ generated by presilting objects containing all projective-injective objects and $\\tau$-perpendicular subca"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2608.13175","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/2608.13175/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"}