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Abstract
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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.
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Keywords
derivator, homotopy theory, abstract homotopy theory,
triangulated categories, homotopy colimits, stable homotopy
theory
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Mathematical Subject Classification 2010
Primary: 55U35, 55U40, 55PXX
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Publication
Received: 13 February 2012
Revised: 9 August 2012
Accepted: 4 September 2012
Published: 25 February 2013
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