{"paper":{"title":"Pseudoskew category algebras and modules over representations of small categories","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.RT","authors_text":"Mawei Wu","submitted_at":"2024-06-28T12:45:56Z","abstract_excerpt":"Let $\\mathcal {C}$ be a small category and let $R$ be a representation of the category $\\mathcal {C}$, that is, a pseudofunctor from a small category to the category of small preadditive categories. In this paper, we mainly study the category $\\mbox{Mod-} R$ of right modules over $R$. We characterize it both as a category of the Abelian group valued functors on $Gr(R)$ and as a category of modules over a new family of algebras: the pseudoskew category algebras $R[{\\mathcal C}]$, where $Gr(R)$ is the linear Grothendieck construction of $R$. Moreover, we also classify the hereditary torsion pair"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2406.19883","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/2406.19883/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"}