The B
            ∞-Structure on the Derived Endomorphism Algebra of the Unit in a Monoidal Category

Wendy Lowen; Michel Van den Bergh

doi:10.1093/imrn/rnab207

The B _∞-Structure on the Derived Endomorphism Algebra of the Unit in a Monoidal Category

Wendy Lowen, Michel Van den Bergh

Onderzoeksoutput: Article › peer review

5 Citaten (Scopus)

Samenvatting

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 -algebra which is -quasi-isomorphic to the derived endomorphism algebra of the tensor unit. This -algebra is obtained as the co-Hochschild complex of a projective resolution of the tensor unit, endowed with a lifted -coalgebra structure. We show that in the classical situation of the category of bimodules over an algebra, this newly defined -algebra is isomorphic to the Hochschild complex of the algebra in the homotopy category of -algebras.

Originele taal-2	English
Pagina's (van-tot)	1690-1729
Aantal pagina's	40
Tijdschrift	International Mathematics Research Notices
Volume	2023
Nummer van het tijdschrift	2
DOI's	https://doi.org/10.1093/imrn/rnab207
Status	Published - 2023

Bibliografische nota

Funding Information:
This work was supported by the Research Foundation Flanders [G.0D86.16N]; the European Union for the ERC [817762-FHiCuNCAG]; and the Russian Academic Excellence Project “5-100.”

Funding Information:
This work was supported by the Research Foundation Flanders [G.0D86.16N]; the European Union

Publisher Copyright:
© The Author(s) 2021. Published by Oxford University Press. All rights reserved.

Copyright:
Copyright 2023 Elsevier B.V., All rights reserved.

Toegang tot document

10.1093/imrn/rnab207

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Citeer dit

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