Fibered Multiderivators and (co)homological descent

TL;DR

This paper develops a theory of fibered multiderivators to improve the understanding of fibrations in triangulated categories and introduces a descent framework for cohomological and homological theories, especially for Grothendieck's six operations.

Contribution

It introduces fibered multiderivators and a descent theory for (co)homology within this framework, advancing the categorical tools for derived and triangulated categories.

Findings

Established a notion of fibered multiderivator.

Developed a cohomological and homological descent theory.

Applied the framework to Grothendieck's six operations.

Abstract

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.