Totalization of simplicial homotopy types

Abstract

We identify the obstructions for the functoriality and the uniqueness of the totalization functor, (partially) defined on the category of simplicial objects in the homotopy category of a stable model category, and we use a result from the cyclic homology of group algebras to show they can be non-zero.

15 pages. The current version extends the constructions and results of the previous version to the homotopy category of an arbitrary stable model category