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)
- 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
gollark: Hmm, how does Nim compare? It also goes through C these days (unless you use nlvm) but things.
gollark: It would be written entirely in Haskell.
gollark: Instead of reading the spec, I would just test it on osmarksmalloc™ and such.
gollark: Maybe *I* should make a C compiler.
gollark: This is a reasonable and correct unit.
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