This is a list of homological algebra topics, by Misplaced Pages page.
Basic techniques
- Cokernel
- Exact sequence
- Chain complex
- Differential module
- Five lemma
- Short five lemma
- Snake lemma
- Nine lemma
- Extension (algebra)
- 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