title: List of homological algebra topics
text: # 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
  