Contents

cohomology

duality

# Contents

## Idea

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

## Properties

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

## 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 $t$-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.