Hochschild cocycle
= Hochschild cocycle
{c}
{title2=$Z^n(A,M)$}
A Hochschild cocycle is a cochain $f$ with $\delta f=0$ in the <Hochschild cochain complex>. For degree two, this is $a\mu(b,c)-\mu(ab,c)+\mu(a,bc)-\mu(a,b)c=0$. It is the condition for <associativity> of a <square-zero extension of an algebra>.