For a morphism of sites such that the corresponding derived direct image and inverse image functor on the derived category of abelian sheaves are related to a further adjoint functor pair .
These together with the internal Ext and Tor functors are often called Grothendieck’s six operations. There is a rich calculus induced by this structure.
A general abstract discussion is in
- H. Fausk, P. Hu, Peter May, Isomorphisms between left and right adjoints (pdf)
The traditional applications are discussed in
Yves Laszlo, Martin Olsson, The six operations for sheaves on Artin stacks I: Finite Coefficients (arXiv:math/0512097)
Yoseph Ayoub, Les six opérations de Grothendieck et le formalisme des cycles évanescants dans le monde motivique PhD thesis, Paris (pdf)
A quick list of the axioms with a Grothendieck’s six operations with an eye towards the definition of motives is in section A.5 of
Revised on December 20, 2012 22:29:02
by Urs Schreiber