Homological algebra is a discipline in algebra and geometry which has been established around 1950 by several authors. The key issues of this theory is
(a) to describe particular objects in a given abelian category like injective or projective modules,
(b) to consider appropriate chain comples to extend a given abelian category,
(c) to introduce and describe derived functors and to establish methods allowing to calculate these on a series of distinguished objects.