Hyperhomology

In homological algebra, the hyperhomology or hypercohomology (${\displaystyle \mathbb {H} _{*}(-),\mathbb {H} ^{*}(-)}$) is a generalization of (co)homology functors which takes as input not objects in an abelian category ${\displaystyle {\mathcal {A}}}$ but instead chain complexes of objects, so objects in ${\displaystyle {\text{Ch}}({\mathcal {A}})}$. It is a sort of cross between the derived functor cohomology of an object and the homology of a chain complex since hypercohomology corresponds to the derived global sections functor ${\displaystyle \mathbf {R} ^{*}\Gamma (-)}$.

Hyperhomology is no longer used much: since about 1970 it has been largely replaced by the roughly equivalent concept of a derived functor between derived categories.