Books & notes

Higher Topos Theory Section 7.4: Geometries from six-functor formalisms

Extension of a six-functor formalism

Proposition 7.30. (Mann–Scholze)

The six-functor formalism \(D\) extends uniquely from \((C,C^{\ad})\) to \((\widetilde C,\widetilde C^{\ad}_0)\).

Proof
See [Mann 2022, Proposition A.5.16] and [Scholze 2025, Proposition 5.16].

References

  1. Lucas Mann. A $p$-Adic 6-Functor Formalism in Rigid-Analytic Geometry. arXiv preprint arXiv:2206.02022. 2022.
  2. Peter Scholze. Six-Functor Formalisms. 2025.