Homological algebra

 is the branch of mathematics that studies homology in a general algebraic setting.

Quotes

 * Homological algebra, conceived as a general tool reaching beyond all special cases, was invented by Cartan and Eilenberg (their book “Homological Algebra” appeared in 1956). This book is a very precise exposition, but limited to the theory of modules over rings and the associated functors “Ext” and “Tor”.