Topological Hochschild homology and the cyclic bar construction in symmetric spectra

TL;DR

This paper clarifies the relationship between two methods for defining topological Hochschild homology in symmetric spectra, correcting a previous error in the comparison between them.

Contribution

It provides a correction to Shipley's comparison of the cyclic bar construction and Bökstedt's construction for topological Hochschild homology in symmetric spectra.

Findings

Corrected the comparison between two definitions of topological Hochschild homology

Clarified the relationship between cyclic bar construction and Bökstedt's construction

Ensured consistency in the theoretical framework for symmetric spectra

Abstract

The cyclic bar construction in symmetric spectra and B\"okstedt's original construction are two possible ways to define the topological Hochschild homology of a symmetric ring spectrum. In this short note we explain how to correct an error in Shipley's original comparison of these two approaches.