The theory of derivators enhances and simplifies the theory of triangulated categories. In this article a notion of fibered (multi)derivator is developed, which similarly enhances fibrations of (monoidal) triangulated categories. We present a theory of cohomological as well as homological descent in this language. The main motivation is a descent theory for Grothendieck's six operations.
Keywords: Derivators, fibered derivators, multiderivators, fibered multicategories, Grothendieck's six-functor-formalism, cohomological descent, homological descent, fundamental localizers, well-generated triangulated categories, equivariant derived categories
2010 MSC: 55U35, 14F05, 18D10, 18D30,18E30, 18G99
Theory and Applications of Categories, Vol. 32, 2017, No. 38, pp 1258-1362.