On the theory of derivators [Elektronische Ressource] / Moritz Groth. Mathematisch-Naturwissenschaftliche Fakultät

On the theory of derivatorsDissertationzurErlangung des Doktorgrades (Dr. rer. nat.)derMathematisch-Naturwissenschaftlichen Fakult atderRheinischen Friedrich-Wilhelms-Universit at Bonnvorgelegt vonMoritz GrothausNeumunsterBonn 2011Angefertigt mit Genehmigung der Mathematisch-Naturwissenschaftlichen Fakult atder Rheinischen Friedrich-Wilhelms-Universit at Bonn1. Gutachter: Prof. Dr. Stefan Schwede2. Gutachter: Prof. Dr. Bernhard KellerTag der Promotion:Erscheinungsjahr:ON THE THEORY OF DERIVATORSMORITZ GROTHAbstract. In Part 1, we develop some aspects of the theory of derivators, pointed deriva-tors, and stable derivators. As a main result, we show that the values of a stable derivatorcan be canonically endowed with the structure of a triangulated category. Moreover, thefunctors belonging to the stable derivator can be turned into exact functors with respectto these triangulated structures. Along the way, we give a simpli cation of the axioms of apointed derivator and a reformulation of the base change axiom in terms of Grothendieck(op) bration. Furthermore, we have a new proof that a combinatorial model categoryhas an underlying derivator.In Part 2, we develop the theory of monoidal derivators and the related notions ofderivators being tensored, cotensored, or enriched over a monoidal derivator. The passagefrom model categories to derivators respects these notions and, hence, gives rise to naturalexamples.