{"paper":{"title":"A remark on fibrancy of ($\\mbox{A$_{\\infty}$Cat}$,$W^{\\tiny\\mbox{A}_{\\infty}}_{\\tiny\\mbox{qe}}$)","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CT","authors_text":"Mattia Ornaghi, Xiaofa Chen","submitted_at":"2024-12-17T21:47:56Z","abstract_excerpt":"In this note we prove the existence, in the category of (strictly unital) A$_{\\infty}$categories, of the pullback of a (strictly unital) A$_{\\infty}$functor, satisfying a particular property (denoted by F1), along any A$_{\\infty}$functor. As a consequence we provide a positive answer to Pascaleff's question whether (A$_{\\infty}$Cat,$W^{\\tiny\\mbox{A}_{\\infty}}_{\\tiny\\mbox{qe}}$) is a fibrant object in RelCat."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2412.13347","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/2412.13347/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"}