A remark on K-theory and S-categories |
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Authors: | Bertrand Toën |
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Institution: | a Laboratoire Emile Picard, UMR CNRS 5580, Université Paul Sabatier, Toulouse, France b Dipartimento di Matematica, Università di Bologna, Italy |
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Abstract: | It is now well known that the K-theory of a Waldhausen category depends on more than just its (triangulated) homotopy category (Invent. Math. 150 (2002) 111). 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? ” |
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Keywords: | 55N15 19D10 18E30 18G55 18D20 |
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