{"paper":{"title":"Higher Koszul duality and $n$-affineness","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AT","math.CT","math.KT"],"primary_cat":"math.AG","authors_text":"Emanuele Pavia, James Pascaleff, Nicol\\`o Sibilla","submitted_at":"2025-03-25T11:00:45Z","abstract_excerpt":"In this paper we study $\\mathbb{E}_n$-Koszul duality in the topological setting, and the closely related question of \\emph{$n$-affineness} for Betti stacks. The $\\mathbb{E}_n$-Koszul dual of the algebra of chains on the $n$-fold loop space of a space $X$ is the algebra of cochains on $X$. It was expected that $\\mathbb{E}_n$-Koszul duality should induce a kind of Morita equivalence between categories of iterated modules, but even the precise formulation of such a statement was not known. We give a rigorous formulation, and a proof, of such an $\\mathbb{E}_n$-Koszul duality in the topological set"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2504.16935","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/2504.16935/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"}