What is "hyperhomology"

In homological algebra, the hyperhomology or hypercohomology of a complex of objects of an abelian category is an extension of the usual homology of an object to complexes. It is a sort of cross between the derived functor cohomology of an object and the homology of a chain complex.

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.