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A remark on K-theory and S-categories | | Bertrand Toen
; Gabriele Vezzosi
; | | Date: |
8 Oct 2002 | | Subject: | K-Theory and Homology; Algebraic Geometry; Algebraic Topology; Category Theory | math.KT math.AG math.AT math.CT | | 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 $K$-theory is not an invariant of triangulated derived categories ?’’ | | Source: | arXiv, math.KT/0210125 | | Services: | Forum | Review | PDF | Favorites | |
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