{"paper":{"title":"Higher Segal spaces and Lax $\\mathbb{A}_\\infty$-algebras","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.CT"],"primary_cat":"math.AT","authors_text":"Adam Gal, Elena Gal","submitted_at":"2019-05-08T22:18:12Z","abstract_excerpt":"The notion of a higher Segal space was introduced by Dyckerhoff and Kapranov as a general framework for studying higher associativity inherent in a wide range of mathematical objects. In the present work we formalize the connection between this notion and the notion of $\\mathbb{A}_\\infty$-algebra. We introduce the notion of a \"$d$-lax $\\mathbb{A}_\\infty$-algebra object\" which generalizes the notion of an $\\mathbb{A}_\\infty$-algebra object. We describe a construction that assigns to a simplicial object $S_\\bullet$ in a category $\\mathscr{S}$ a datum of higher associators. We show that this datu"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1905.03376","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":""},"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"}