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 *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