List of homological algebra topics

This is a list of homological algebra topics, by Wikipedia page.

Basic techniques

 * Cokernel
 * Exact sequence
 * Chain complex
 * Differential module
 * Five lemma
 * Short five lemma
 * Snake lemma
 * Nine lemma
 * Extension (algebra)
 * Central extension
 * Splitting lemma
 * Projective module
 * Injective module
 * Projective resolution
 * Injective resolution
 * Koszul complex
 * Exact functor
 * Derived functor
 * Ext functor
 * Tor functor
 * Filtration (abstract algebra)
 * Spectral sequence
 * Abelian category
 * Triangulated category
 * Derived category

Applications

 * Group cohomology
 * Galois cohomology
 * Lie algebra cohomology
 * Sheaf cohomology
 * Whitehead problem
 * Homological conjectures in commutative algebra