A cochain complex is a sequence of Abelian groups or modules 
with group homomorphisms
or module homomorphisms, respectively, 
satisfying 
. Its 
th cohomology group is
.
Cochain Complex
See also
Chain Complex, Coboundary, Coboundary Expander, Coboundary Operator, Cohomology Group, Homomorphism, Singular CohomologyExplore with Wolfram|Alpha
References
Hatcher, A. Algebraic Topology. Cambridge, England: Cambridge University Press, 2002.Cite this as:
Weisstein, Eric W. "Cochain Complex." From MathWorld--A Wolfram Resource. https://mathworld.wolfram.com/CochainComplex.html