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