{"paper":{"title":"Deligne categories and the limit of categories $Rep(GL(m|n))$","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.RT","authors_text":"Inna Entova-Aizenbud, Vera Serganova, Vladimir Hinich","submitted_at":"2015-11-24T13:38:48Z","abstract_excerpt":"For each integer $t$ a tensor category $V_t$ is constructed, such that exact tensor functors $V_t \\longrightarrow C$ classify dualizable $t$-dimensional objects in $C$ not annihilated by any Schur functor. This means that $V_t$ is the \"abelian envelope\" of the Deligne category $Rep(GL_t)$. Any tensor functor $Rep(GL_t)\\longrightarrow C$ is proved to factor either through $V_t$ or through one of the classical categories $Rep(GL(m|n))$ with $m-n=t$. The universal property of $V_t$ implies that it is equivalent to the categories\n  $Rep_{Rep(GL_{t_1})\\otimes Rep(GL_{t_2})}(GL(X),\\epsilon)$, ($t=t_"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1511.07699","kind":"arxiv","version":7},"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/1511.07699/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"}