KnowraChain complexLinked fromLinked fromThe 9 pages that link to Chain complex, each with the reason it gives.All 9Broader topic 1Related 2Narrower topic 4Compared with 2Algebraic topologyRelated: Its cycles and boundaries provide the algebraic machinery behind homology groups.Homological algebraBroader topic: Chain complexes are the basic structures whose homology homological algebra computes.Homology groupNarrower topic: Homology groups are computed from the kernels and images of consecutive maps in a chain complex.Exact sequenceCompared with: It imposes containment of image in kernel, while exactness strengthens this to equality.Chain (order theory)Compared with: Despite sharing the word, this algebraic construction is not a chain in a partially ordered set.Generalized Stokes theoremRelated: The identity that the boundary of a boundary vanishes underlies the theorem’s boundary structure.Simplicial complexNarrower topic: The simplicial chain complex is a special case of this general algebraic structure.Eilenberg–Zilber theoremNarrower topic: The theorem compares two chain complexes through chain maps and homotopies.Zig-zag lemmaNarrower topic: The lemma starts with three chain complexes and maps that respect their differentials.