{"paper":{"title":"A higher homological approach to the $q$-characters of representations of quantum affine algebras","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["math.CO","math.CT"],"primary_cat":"math.RT","authors_text":"\\'Elie Casbi","submitted_at":"2026-05-27T16:14:25Z","abstract_excerpt":"For any acyclic quiver $Q$ without multiple edges, we construct a monoidal category $\\mathcal{R}_Q$ whose indecomposable objects are tensor products (over the base field) of finite-dimensional modules over the path algebra of $Q$. We show the existence and uniqueness up to homotopy of certain distinguished chain complexes satisfying good homological properties (higher almost split complexes) preserved under tensoring by objects in $\\mathcal{R}_Q$. As a crucial ingredient for this construction, we establish the existence of a family of complete exceptional sequences in $\\mathrm{mod}\\,\\mathbf{k}"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2605.28682","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/2605.28682/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"}