{"paper":{"title":"$\\omega$-weak equivalences between weak $\\omega$-categories","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CT","authors_text":"Keisuke Hoshino, Soichiro Fujii, Yuki Maehara","submitted_at":"2024-06-19T06:06:04Z","abstract_excerpt":"We study $\\omega$-weak equivalences between weak $\\omega$-categories in the sense of Batanin-Leinster. Our $\\omega$-weak equivalences are strict $\\omega$-functors satisfying essential surjectivity in every dimension, and when restricted to those between strict $\\omega$-categories, they coincide with the weak equivalences in the model category of strict $\\omega$-categories defined by Lafont, M\\'etayer, and Worytkiewicz. We show that the class of $\\omega$-weak equivalences has the 2-out-of-3 property. We also consider a generalisation of $\\omega$-weak equivalences, defined as weak $\\omega$-funct"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2406.13240","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/2406.13240/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"}