Volume 13, issue 1 (2013)

Download this article
Download this article For screen
For printing
Recent Issues

Volume 17
Issue 6, 3213–3852
Issue 5, 2565–3212
Issue 4, 1917–2564
Issue 3, 1283–1916
Issue 2, 645–1281
Issue 1, 1–643

Volume 16, 6 issues

Volume 15, 6 issues

Volume 14, 6 issues

Volume 13, 6 issues

Volume 12, 4 issues

Volume 11, 5 issues

Volume 10, 4 issues

Volume 9, 4 issues

Volume 8, 4 issues

Volume 7, 4 issues

Volume 6, 5 issues

Volume 5, 4 issues

Volume 4, 2 issues

Volume 3, 2 issues

Volume 2, 2 issues

Volume 1, 2 issues

The Journal
About the Journal
Subscriptions
Editorial Board
Editorial Interests
Editorial Procedure
Submission Guidelines
Submission Page
Author Index
To Appear
ISSN (electronic): 1472-2739
ISSN (print): 1472-2747
Derivators, pointed derivators and stable derivators

Moritz Groth

Algebraic & Geometric Topology 13 (2013) 313–374
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/