Koszul homotopy for multiplication by a generator
= Koszul homotopy for multiplication by a generator
{c}
{title2=$\partial h_j+h_j\partial=f_j\operatorname{id}$}
Exterior multiplication $h_j(u)=e_j\wedge u$ is a <chain homotopy> between multiplication by $f_j$ and zero on a <Koszul complex>. A linear combination of these homotopies is a <contracting homotopy> when the generators span the unit ideal.