Derivator SixFunctorFormalisms  Construction II
Abstract
Starting from very simple and obviously necessary axioms on a (derivator enhanced) fourfunctorformalism, we construct derivator sixfunctorformalisms using compactifications. This works, for example, for various contexts over topological spaces and algebraic schemes alike. The formalism of derivator sixfunctorformalisms not only encodes all isomorphisms between compositions of the six functors (and their compatibilities) but also the interplay with pullbacks along diagrams and homotopy Kan extensions. One could say: a ninefunctorformalism. Such a formalism allows to extend sixfunctorformalisms to stacks using (co)homological descent. The input datum can, for example, be obtained from a fibration of monoidal model categories.
 Publication:

arXiv eprints
 Pub Date:
 February 2019
 arXiv:
 arXiv:1902.03625
 Bibcode:
 2019arXiv190203625H
 Keywords:

 Mathematics  Algebraic Geometry;
 Mathematics  Category Theory;
 55U35;
 14F05;
 18D10;
 18D30;
 18E30;
 18G99