Homological algebra is the branch of mathematics that studies homology in a general algebraic setting. It is a relatively young discipline, whose origins...

This is a list of homological algebra topics, by Wikipedia page. Cokernel Exact sequence Chain complex Differential module Five lemma Short five lemma...

In homological algebra, a monad is a 3-term complex A → B → C of objects in some abelian category whose middle term B is projective, whose first map A → B...

In homological algebra and algebraic topology, a spectral sequence is a means of computing homology groups by taking successive approximations. Spectral...

In mathematics, homological conjectures have been a focus of research activity in commutative algebra since the early 1960s. They concern a number of...

of modern algebraic geometry. His research extended the scope of the field and added elements of commutative algebra, homological algebra, sheaf theory...

(not only algebraic ones). At its origin, it was introduced, together with homological algebra for allowing the algebraic study of non-algebraic objects...

In mathematics, and more specifically in homological algebra, a resolution (or left resolution; dually a coresolution or right resolution) is an exact...

In homological algebra, the mapping cone is a construction on a map of chain complexes inspired by the analogous construction in topology. In the theory...

right R-module M. The concept of torsion plays an important role in homological algebra. If M and N are two modules over a commutative domain R (for example...