Open Access
2015 On Determinant Functors and $K$-Theory
Fernando Muro, Andrew Tonks, Malte Witte
Publ. Mat. 59(1): 137-233 (2015).


We extend Deligne's notion of determinant functor to Waldhausen categories and (strongly) triangulated categories. We construct explicit universal determinant functors in each case, whose target is an algebraic model for the $1$-type of the corresponding $K$-theory spectrum. As applications, we answer open questions by Maltsiniotis and Neeman on the $K$-theory of (strongly) triangulated categories and a question of Grothendieck to Knudsen on determinant functors. We also prove additivity theorems for low-dimensional $K$-theory of (strongly) triangulated categories and obtain generators and (some) relations for various $K_{1}$-groups. This is achieved via a unified theory of determinant functors which can be applied in further contexts, such as derivators.


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Fernando Muro. Andrew Tonks. Malte Witte. "On Determinant Functors and $K$-Theory." Publ. Mat. 59 (1) 137 - 233, 2015.


Published: 2015
First available in Project Euclid: 21 January 2015

zbMATH: 1307.44008
MathSciNet: MR3302579

Primary: 18E10 , 18E30 , 18F25 , 18G50 , 18G55 , 19A99 , 19B99

Keywords: Determinant functor , exact category , Grothendieck derivator , ‎K-theory , triangulated category , Waldhausen category

Rights: Copyright © 2015 Universitat Autònoma de Barcelona, Departament de Matemàtiques

Vol.59 • No. 1 • 2015
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