The universal six-functor formalism

Abstract

We prove that Morel-Voevodsky's stable ${\mathbb{A}}^1$-homotopy theory affords the universal coefficient system, giving rise to Grothendieck's six operations.

50 pages; v2: new introduction, other minor changes; v3: accepted version; v4: corrects a small mistake in published version

References in corpus (4)

• The six operations in equivariant motivic homotopy theory
• Mixed Weil cohomologies
• Adjoint functor theorems for $\infty$-categories
• Motivic Hodge modules

Cited by in corpus (11)

• On the Nori and Hodge realisations of Voevodsky motives
• Global homotopy theory via partially lax limits
• Tensor structure on perverse Nori motives
• Cohomological Hall algebras and vertex algebras
• Tensor structures on fibered categories
• Derivator Six-Functor-Formalisms -- Construction II
• Constructing monoidal structures on fibered categories via factorizations
• Mixed Hodge modules on stacks
• An introduction to six-functor formalisms
• Trace maps in motivic homotopy and local terms
• An axiomatization of six-functor formalisms