{"paper":{"title":"Homotopy-coherent algebra via Segal conditions","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.CT"],"primary_cat":"math.AT","authors_text":"Hongyi Chu, Rune Haugseng","submitted_at":"2019-07-09T04:17:02Z","abstract_excerpt":"Many homotopy-coherent algebraic structures can be described by Segal-type limit conditions determined by an \"algebraic pattern\", bywhich we mean an $\\infty$-category equipped with a factorization system and a collection of \"elementary\" objects. Examples of structures that occur as such \"Segal $\\mathcal{O}$-spaces\" for an algebraic pattern $\\mathcal{O}$ include $\\infty$-categories, $(\\infty,n)$-categories, $\\infty$-operads, $\\infty$-properads, and algebras for an $\\infty$-operad in spaces.\n  In the first part of this paper we set up a general frameworkn for algebraic patterns and their Segal o"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1907.03977","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/1907.03977/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"}