Fritz Hörmann
Published 2019-02-10Version 1
Starting from very simple and obviously necessary axioms on a (derivator enhanced) four-functor-formalism, we construct derivator six-functor-formalisms using compactifications. This works, for example, for various contexts over topological spaces and algebraic schemes alike. The formalism of derivator six-functor-formalisms 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 nine-functor-formalism. Such a formalism allows to extend six-functor-formalisms to stacks using (co)homological descent. The input datum can, for example, be obtained from a fibration of monoidal model categories.
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