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 Homological algebra