{"paper":{"title":"Derived Lie $\\infty$-groupoids and algebroids in higher differential geometry","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["math.AG","math.AT"],"primary_cat":"math.DG","authors_text":"Qingyun Zeng","submitted_at":"2022-10-12T01:44:39Z","abstract_excerpt":"We study various problems arising in higher differential geometry using {\\it derived Lie $\\infty$-groupoids and algebroids}.We first study Lie $\\infty$-groupoids in various categories of derived geometric objects in differential geometry, including derived manifolds, derived analytic spaces, derived noncommutative spaces, and derived Banach manifolds. We construct category of fibrant objects (CFO) structures in the category of derived Lie $\\infty$-groupoids. Then we study $L_{\\infty}$-algebroids which are the infinitesimal counterpart of derived Lie $\\infty$-groupoids. We then study the homoto"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2210.05856","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/2210.05856/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"}