Chain complex

In homological algebra, a chain complex is a sequence of abelian groups or modules A₀, A₁, A₂... connected by homomorphisms d_n : A_n -> A_n-1, such that the composition of any two consecutive maps is zero: d_n o d_n+1 = 0 for all n. Chain complexes are mainly used to define homology and cohomology.

Examples from topology, group theory...