# nLab hyper-derived functor

### Context

#### Homological algebra

homological algebra

and

nonabelian homological algebra

diagram chasing

model category

for ∞-groupoids

# 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 objects 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.

Revised on August 26, 2012 19:19:23 by Urs Schreiber (89.204.137.239)