{"paper":{"title":"Morphisms of A-infinity Bialgebras and Applications","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.KT"],"primary_cat":"math.AT","authors_text":"Ronald Umble, Samson Saneblidze","submitted_at":"2011-06-25T01:25:33Z","abstract_excerpt":"We define the notion of a relative matrad and realize the free relative matrad as a free H_\\infty-bimodule structure on cellular chains of bimultiplihedra JJ={JJ_{n,m} = JJ_{m,n}}. We define a morphism G:A => B of A_\\infty-bialgebras as a bimodule over H_\\infty and prove that the homology of every A_\\infty-bialgebra over a commutative ring with unity admits an induced A_\\infty-bialgebra structure. We extend the Bott-Samelson isomorphism to an isomorphism of A_\\infty-bialgebras and identify the A_\\infty-bialgebra structure of H_*(\\Omega\\Sigma X; Q). For each n>1, we construct a space X_n and id"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1106.5090","kind":"arxiv","version":5},"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"}