# 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.