Sequence of abelian groups (or modules) Cₙ with boundary maps ∂ₙ: Cₙ → Cₙ₋₁ satisfying ∂ₙ ∘ ∂ₙ₊₁ = 0. The primitive object of homological algebra; homology Hₙ = ker ∂ₙ / im ∂ₙ₊₁ measures failure of exactness.
Chain complex
Related concepts
- Ring (R, +, ·)
- Abelian category
- Exact sequence
- Cochain complex and cohomology
- Tor functor
- Ext functor
- Projective resolution
- Snake lemma
- Long exact sequence in (co)homology
- Spectral sequence
- Derived functor
- Grothendieck spectral sequence
- Künneth formula
- Mayer-Vietoris sequence
- Zig-zag (connecting homomorphism) lemma
- Euler characteristic of a chain complex
- Projective dimension
- Koszul complex
- Cartan–Eilenberg resolution
- Stora–Zumino descent equations (gauge anomalies)