Abstract
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.
| Original language | English |
|---|---|
| Pages (from-to) | 1690-1729 |
| Number of pages | 40 |
| Journal | International Mathematics Research Notices |
| Volume | 2023 |
| Issue number | 2 |
| DOIs | |
| Publication status | Published - 2023 |
Bibliographical note
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.