A telescope comparison lemma for THH

with Mike Mandell

ABSTRACT. The usual telescope or sequential homotopy colimit construction of the underlying infinite loop space must be replaced for symmetric spectra by a homotopy colimit over the category of finite sets and injections as shown in Symmetric spectra and topological Hochschild homology by the second author. Here we show that for convergent symmetric spectra this modified homotopy colimit agrees with the usual telescope construction. This sharpens Bokstedt's original lemma because no connectivity conditions are necessary here.