Vol. 2, No. 2, 2017

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$K\mkern-2mu$-theory of derivators revisited

Fernando Muro and George Raptis

Vol. 2 (2017), No. 2, 303–340
Abstract

We define a K-theory for pointed right derivators and show that it agrees with Waldhausen K-theory in the case where the derivator arises from a good Waldhausen category. This K-theory is not invariant under general equivalences of derivators, but only under a stronger notion of equivalence that is defined by considering a simplicial enrichment of the category of derivators. We show that derivator K-theory, as originally defined, is the best approximation to Waldhausen K-theory by a functor that is invariant under equivalences of derivators.

Keywords
$K\mkern-2mu$-theory, derivator
Mathematical Subject Classification 2010
Primary: 19D99, 55U35
Milestones
Received: 30 October 2015
Accepted: 21 June 2016
Published: 14 December 2016
Authors
Fernando Muro
Facultad de Matemáticas, Departamento de Álgebra
Universidad de Sevilla
Avda. Reina Mercedes s/n
41012 Sevilla
Spain
George Raptis
Fakultät für Mathematik
Universität Regensburg
93040 Regensburg
Germany