Fibered Multiderivators and (co)homological descent

2015/05/05 by Fritz Hörmann, Hörmann, Fritz
Mathematics · #14F05 #18D10 #18D30 #18E30 #18G99 #55U35 #Algebraic Geometry (math.AG) #Algebraic Topology (math.AT) #Category Theory (math.CT) #FOS: Mathematics #math.AG #math.AT #math.CT #msc:14F05 #msc:18D10 #msc:18D30 #msc:18E30 #msc:18G99 #msc:55U35

paper · pdf · doi:10.48550/arxiv.1505.00974

88 pages

arxiv created 2015/11/24 · arxiv updated 2015/11/25

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.

Related

• Derivator Six Functor Formalisms -- Definition and Construction I
• Six Functor Formalisms and Fibered Multiderivators
• Enlargement of (fibered) derivators
• Notes on Grothendieck topologies, fibered categories and descent theory
• Fibered Multicategory Theory