{"paper":{"title":"The universal Hall bialgebra of a double 2-Segal space","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AG","math.CT"],"primary_cat":"math.AT","authors_text":"Mark D Penney","submitted_at":"2017-11-28T09:20:24Z","abstract_excerpt":"Hall algebras and related constructions have had diverse applications in mathematics and physics, ranging from representation theory and quantum groups to Donaldson-Thomas theory and the algebra of BPS states. The theory of $2$-Segal spaces was introduced independently by Dyckerhoff-Kapranov and G\\'alvez-Carrillo-Kock-Tonks as a unifying framework for Hall algebras: every $2$-Space defines an algebra in the $\\infty$-category of spans, and different Hall algebras correspond to different linearisations of this universal Hall algebra.\n  A recurring theme is that Hall algebras can often be equippe"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1711.10194","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":""},"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"}