Derivator Six-Functor-Formalisms -- Construction II

Abstract

Starting from simple and necessary axioms on a (derivator enhanced) four-functor-formalism, we construct derivator six-functor-formalisms using compactifications. This works, for instance, for the stable homotopy categories of Morel-Voevodsky-Ayoub, and also for the classical setting of unbounded complexes of sheaves of Abelian groups on `nice' topological spaces. The formalism of derivator six-functor-formalisms elegantly encodes all isomorphisms between compositions of the six functors (and their compatibilities) and moreover it gives coherent enhancements over diagrams of correspondences. Such a formalism allows to extend six-functor-formalisms to stacks using (co)homological descent.

completely revised version now including the discussion of main examples

References in corpus (4)

• The linearity of traces in monoidal categories and bicategories
• The universal six-functor formalism
• Motivic Hodge modules
• Derivator Six Functor Formalisms -- Definition and Construction I

Cited by in corpus (3)

• Cotorsion Pairs and Quillen Adjunctions
• Higher stacks as diagrams
• Grothendieck Duality theories -- abstract and concrete, I: pseudo-coherent finite maps