Derivators, pointed derivators, and stable derivators

Details Derivators, pointed derivators, and stable derivators Derivators, pointed derivators, and stable derivators

2011-12-16

arxiv.org/abs/1112.3840v2

Mathematics

Algebraic Topology

Minor misconception in the context of adjunctions of derivators removed, Section 2 slightly reorganized, exposition polished,

Scientific paper

We develop some aspects of the theory of derivators, pointed derivators, and stable derivators. As a main result, we show that the values of a stable derivator can be canonically endowed with the structure of a triangulated category. Moreover, the functors belonging to the stable derivator can be turned into exact functors with respect to these triangulated structures. Along the way, we give a simplification of the axioms of a pointed derivator and a reformulation of the base change axiom in terms of Grothendieck (op)fibration. Furthermore, we have a new proof that a combinatorial model category has an underlying derivator.

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