Derivators, pointed derivators, and stable derivators
Abstract
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.
Cite
@article{arxiv.1112.3840,
title = {Derivators, pointed derivators, and stable derivators},
author = {Moritz Groth},
journal= {arXiv preprint arXiv:1112.3840},
year = {2014}
}
Comments
Minor misconception in the context of adjunctions of derivators removed, Section 2 slightly reorganized, exposition polished, submitted for publication