Derivators, pointed derivators and stable derivators

Groth, Moritz

doi:10.2140/agt.2013.13.313

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Derivators, pointed derivators and stable derivators

Moritz Groth

Algebraic & Geometric Topology 13 (2013) 313–374

DOI: 10.2140/agt.2013.13.313

Abstract

We develop some aspects of the theory of derivators, pointed derivators and stable derivators. Stable derivators are shown to canonically take values in triangulated categories. Similarly, the functors belonging to a stable derivator are canonically exact so that stable derivators are an enhancement of triangulated categories. We also establish a similar result for additive derivators in the context of pretriangulated categories. Along the way, we simplify the notion of a pointed derivator, reformulate the base change axiom and give a new proof that a combinatorial model category has an underlying derivator.

Keywords

derivator, homotopy theory, abstract homotopy theory, triangulated categories, homotopy colimits, stable homotopy theory

Mathematical Subject Classification 2010

Primary: 55U35, 55U40, 55PXX

References

Publication

Received: 13 February 2012

Revised: 9 August 2012

Accepted: 4 September 2012

Published: 25 February 2013

Authors

Moritz Groth
Radboud University Nijmegen Heyendaalseweg 135 6525 AJ Nijmegen Netherlands
http://www.math.ru.nl/~mgroth/

Volume 13, issue 1 (2013)