List of homological algebra topics
# 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
