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We prove the additivity theorem for the K-theory of triangulated derivators. This solves one of the conjectures made by Maltsiniotis in [G. Maltsiniotis, La K-théorie d'un dérivateur triangulé, in: Alexei Davydov, Michael Batanin, Michael Johnson, Stephen Lack, Amnon Neeman (Eds.), Categories in Algebra, Geometry and Physics, Conference and Workshop in honor of Ross Street's 60th Birthday, in: Contemp. Math., vol. 431, Amer. Math. Soc., 2007, pp. 341-368]. We also review some basic definitions and results in the theory of derivators in the sense of Grothendieck. 相似文献
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Denis-Charles Cisinski 《Journal of Pure and Applied Algebra》2002,174(1):43-82
The purpose of these notes is to give an ad hoc construction of a closed model category structure on a topos inverting an arbitrary small set of arrows. Moreover, a necessary and sufficient condition for those structures to be proper is given. As an example, the Joyal closed model category structure on the category of simplicial objects of a topos is constructed without the use of (boolean) points. 相似文献
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