A remark on K -theory and S -categories.
Résumé
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 ?''
Origine : Fichiers produits par l'(les) auteur(s)
Loading...