Elsevier

Advances in Mathematics

Volume 217, Issue 4, 1 March 2008, Pages 1381-1475
Advances in Mathematics

Additivity for derivator K-theory

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Abstract

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.

Keywords

K-theory
Derivators

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