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Title: | The B-infinity-Structure on the Derived Endomorphism Algebra of the Unit in a Monoidal Category | Authors: | Lowen, Wendy VAN DEN BERGH, Michel |
Issue Date: | 2023 | Publisher: | OXFORD UNIV PRESS | Source: | INTERNATIONAL MATHEMATICS RESEARCH NOTICES, 2023 (2), p. 1690-1729 | Abstract: | Consider a monoidal category that 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-infinity-algebra that is A(infinity)-quasi-isomorphic to the derived endomorphism algebra of the tensor unit. This B-infinity-algebra is obtained as the co-Hochschild complex of a projective resolution of the tensor unit, endowed with a lifted A(infinity)-coalgebra structure. We show that in the classical situation of the category of bimodules over an algebra, this newly defined B-infinity-algebra is isomorphic to the Hochschild complex of the algebra in the homotopy category of B-infinity-algebras. | Notes: | van den Bergh, M (corresponding author), Univ Hasselt, Campus Diepenbeek,Agoralaan Gebouw D, B-3590 Diepenbeek, Belgium.; van den Bergh, M (corresponding author), Free Univ Brussels, Dept Math & Data Sci, Pleinlaan 2, B-1050 Brussels, Belgium. michel.vandenbergh@uhasselt.be |
Document URI: | http://hdl.handle.net/1942/37464 | ISSN: | 1073-7928 | e-ISSN: | 1687-0247 | DOI: | 10.1093/imrn/rnab207 | ISI #: | 000790105800001 | Rights: | The Author(s) 2021. Published by Oxford University Press. All rights reserved. For permissions, please e-mail: journals.permission@oup.com. | Category: | A1 | Type: | Journal Contribution | Validations: | ecoom 2023 |
Appears in Collections: | Research publications |
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