nLab
hyper-derived functor
Contents
Context
Homological algebra
Model category theory
model category

Definitions
Morphisms
Universal constructions
Refinements
Producing new model structures
Presentation of $(\infty,1)$ -categories
Model structures
for $\infty$ -groupoids
for ∞-groupoids

for $n$ -groupoids
for $\infty$ -groups
for $\infty$ -algebras
general
specific
for stable/spectrum objects
for $(\infty,1)$ -categories
for stable $(\infty,1)$ -categories
for $(\infty,1)$ -operads
for $(n,r)$ -categories
for $(\infty,1)$ -sheaves / $\infty$ -stacks
Contents
Idea
In the context of homological algebra derived functors are traditionally considered on a model structure on chain complexes and often they are evaluated only on chain complexes that are concentrated in a single degree. If instead they are evaluated on general chain complexes, one sometimes speaks of hyper-derived functors for emphasis.

For more see at derived functor in homological algebra .

Examples
If abelian sheaf cohomology is considered in terms of the derived functor of the global section functor, then the corresponding hyper-derived functor is hypercohomology . This, too, is really just the basic definition of (abelian) cohomology , but not restricted to Eilenberg-MacLane object s concentrated in a single degree.

Properties
There is a certain spectral sequence that can help to compute values of hyper-derived functors. See the section Spectral sequences for hyper-derived functors .

Last revised on August 26, 2012 at 19:19:23.
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