Singular cochain
= Singular cochain
{title2=$C^n(X;A)$}
A singular $n$-cochain with coefficients in an <abelian group> $A$ is a homomorphism from the <singular chain group> $C_n(X;\mathbb Z)$ to $A$. It is specified by its values on all singular simplices, without a finite-support restriction. Its <coboundary> evaluates on the alternating sum of the faces. The resulting <cochain complex> computes <singular cohomology>.