http://nlab.mathforge.org/nlab/show/derivator
Groth: Monoidal derivators and additive derivators
arXiv:1101.4144 Homotopical exact squares and derivators from arXiv Front: math.CT by Georges Maltsiniotis The aim of this paper is to generalize in a homotopical framework the notion of exact square introduced by René Guitart, and explain the relationship between this generalization and the theory of derivators.
[arXiv:1212.3277] The additivity of traces in monoidal derivators from arXiv Front: math.AT by Moritz Groth, Kate Ponto, Michael Shulman We develop the theory of monoidal structures on derivators, culminating in a proof that generalized trace maps in a closed symmetric monoidal stable derivator are additive along distinguished triangles. This includes the additivity of classical Euler characteristics and Lefschetz numbers, as well as many generalizations of these invariants
The proof of additivity closely follows that of May for triangulated categories, but the derivator context makes the underlying ideas more transparent, showcasing the advantages of derivators over triangulated categories, model categories, and (infinity,1)-categories. We expect many other generalizations of classical stable results to be possible in this context as well.
nLab page on Derivator