English (United Kingdom)

https://curated-unify.zendy.io/wp-json/zendy-region/v1/featured_content/oa?rat=en

https://curated-unify.zendy.io/wp-json/zendy-region/v1/highlighted_journal/

Global: Zendy Tools annual

Presents the keyphrase highlighting as premium feature

Keyphrase Highlighting

Presents the summarisation as premium feature

Summarisation

Insights

Presents the pdf analysis as premium feature

PDF Analysis

Presents the zaia usage as premium feature

ZAIA

Global: Zendy Tools monthly

Global: Zendy Plus monthly

Presents the access of premium content as premium feature

Premium Content

Global: Zendy Plus annual

Global: Zendy Free Plan

The notion of Hochschild homology of a dg algebra admits a naturaldualization, the coHochschild homology of a dg coalgebra, introduced inarXiv:0711.1023 by Hess, Parent, and Scott as a tool to study free loop spaces.In this article we prove "agreement" for coHochschild homology, i.e., that thecoHochschild homology of a dg coalgebra $C$ is isomorphic to the Hochschildhomology of the dg category of appropriately compact $C$-comodules, from whichMorita 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 ofthe suspension spectrum of a space $X$ is equivalent to the suspension spectrumof the free loop space on $X$, as long as $X$ is a nice enough space (forexample, simply connected.) Based on this result and on a Quillen equivalenceestablished by the authors in arXiv:1402.4719, we prove that "agreement" holdsfor coTHH as well.

Invariance properties of coHochschild homology