nLab
Verdier-Grothendieck context

Context

Geometry

Cohomology

cohomology

Special and general types

Special notions

Variants

Extra structure

Operations

Theorems

Duality

Contents

Idea

The specialization of a context of six operations (f *f *)(f^\ast \dashv f_\ast), (f !f !)(f_! \dashv f^!) to the case that the “projection formulaYf !Xf !(f *YX)Y \otimes f_! X \simeq f_!(f^\ast Y \otimes X) holds naturally in X,YX,Y. (May 05, def. 2.12)

Properties

In a Verdier-Grothendieck context, duality intertwines f !f_! with f *f_\ast and f !f^! with f *f^\ast.

(May 05, section 3, Joshua, corollary 5.4)

References

A general abstract discussion of the axioms and their consequences is in

  • H. Fausk, P. Hu, Peter May, Isomorphisms between left and right adjoints, Theory and Applications of Categories , Vol. 11, 2003, No. 4, pp 107-131. (TAC, pdf)

A fairly general class of implementations is in

  • Roy Joshua, Grothendieck-Verdier duality in enriched symmetric monoidal tt-categories (pdf)

Last revised on February 9, 2014 at 09:18:37. See the history of this page for a list of all contributions to it.