(also nonabelian homological algebra)
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model category, model $\infty$-category
Definitions
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Presentation of $(\infty,1)$-categories
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for $\infty$-groupoids
on chain complexes/model structure on cosimplicial abelian groups
related by the Dold-Kan correspondence
for equivariant $\infty$-groupoids
for rational $\infty$-groupoids
for rational equivariant $\infty$-groupoids
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general $\infty$-algebras
specific $\infty$-algebras
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
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.
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.
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. See the history of this page for a list of all contributions to it.