A remark on K -theory and S -categories.

Bertrand Toen (1) , Gabriele Vezzosi

1 LEP - Laboratoire Émile Picard

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 $K$-theory is not an invariant of triangulated derived categories ?''

Domaines: Catégories et ensembles [math.CT]; K-théorie et homologie [math.KT]

Bertrand Toen, Gabriele Vezzosi. A remark on K -theory and S -categories.. Topology, 2004, 43 (4), pp.765-791. ⟨10.1016/j.top.2003.10.008⟩. ⟨hal-00773020⟩