Derivators, pointed derivators and stable derivators

Groth, Moritz¹

¹Radboud University Nijmegen, Heyendaalseweg 135, 6525 AJ Nijmegen, Netherlands

Algebraic and Geometric Topology, Tome 13 (2013) no. 1, pp. 313-374

Résumé

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.

Détail

DOI : 10.2140/agt.2013.13.313

Classification : 55U35, 55U40, 55PXX
Keywords: derivator, homotopy theory, abstract homotopy theory, triangulated categories, homotopy colimits, stable homotopy theory

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