A remark on K-theory and S-categories
arXiv:math/0210125
Abstract
It is now well known that the K-theory of a Waldhausen category depends on more than just its (triangulated) homotopy category (see [Schlichting]). The purpose of this note is to show that the K-theory spectrum of a (good) Waldhausen category is completely determined by its Dwyer-Kan simplicial localization, without any additional structure. As the simplicial localization is a refined version of the homotopy category which also determines the triangulated structure, our result is a possible answer to the general question: ``To which extent -theory is not an invariant of triangulated derived categories ?''
23 pages; final version, accepted for publication in 'Topology'