A remark on K -theory and S -categories.
Toen, Bertrand ; Vezzosi, Gabriele
HAL, hal-00773020 / Harvested from HAL
Text on HAL
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 ?''
Publié le : 2004-07-07
Classification:  [MATH.MATH-CT]Mathematics [math]/Category Theory [math.CT],  [MATH.MATH-KT]Mathematics [math]/K-Theory and Homology [math.KT] 
@article{hal-00773020,
     author = {Toen, Bertrand and Vezzosi, Gabriele},
     title = {A remark on K -theory and S -categories.},
     journal = {HAL},
     volume = {2004},
     number = {0},
     year = {2004},
     language = {en},
     url = {http://dml.mathdoc.fr/item/hal-00773020}
}

Toen, Bertrand; Vezzosi, Gabriele. A remark on K -theory and S -categories.. HAL, Tome 2004 (2004) no. 0, . http://gdmltest.u-ga.fr/item/hal-00773020/