Invariance properties of coHochschild homology

JOURNAL OF PURE AND APPLIED ALGEBRA

卷:225

Article

Hess, Kathryn¹  Shipley, Brooke² 

[1] EPFL SV BMI UPHESS, Stn 8, CH-1015 Lausanne, Switzerland

[2] Univ Illinois, Dept Math Stat & Comp Sci, 508 SEC M-C 249,851 S Morgan St, Chicago, IL 60607 USA

关键词: Topological Hochschild homology;    Coalgebras;   

DOI  :  10.1016/j.jpaa.2020.106505

来源: Elsevier

【 摘 要 】

The notion of Hochschild homology of a dg algebra admits a natural dualization, the coHochschild homology of a dg coalgebra, introduced in [23] as a tool to study free loop spaces. In this article we prove agreement for coHochschild homology, i.e., that the coHochschild homology of a dg coalgebra C is isomorphic to the Hochschild homology of the dg category of appropriately compact C-comodules, from which Morita invariance of coHochschild homology follows. Generalizing the dg case, we define the topological coHochschild homology (coTHH) of coalgebra spectra, of which suspension spectra are the canonical examples, and show that coTHH of the suspension spectrum of a space X is equivalent to the suspension spectrum of the free loop space on X, as long as X is a nice enough space (for example, simply connected.) Based on this result and on a Quillen equivalence established in [21], we prove that agreement holds for coTHH as well. (C) 2020 Elsevier B.V. All rights reserved.

【 授权许可】

Free