{"paper":{"title":"The $B_\\infty$-structure on the derived endomorphism algebra of the unit in a monoidal category","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.KT","authors_text":"Michel Van den Bergh, Wendy Lowen","submitted_at":"2019-07-13T08:21:36Z","abstract_excerpt":"Consider a monoidal category which is at the same time abelian with enough projectives and such that projectives are flat on the right. We show that there is a $B_{\\infty}$-algebra which is $A_{\\infty}$-quasi-isomorphic to the derived endomorphism algebra of the tensor unit. This $B_{\\infty}$-algebra is obtained as the co-Hochschild complex of a projective resolution of the tensor unit, endowed with a lifted $A_{\\infty}$-coalgebra structure. We show that in the classical situation of the category of bimodules over an algebra, this newly defined $B_{\\infty}$-algebra is isomorphic to the Hochsch"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1907.06026","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"}