Let $X$ be a simplicial set and $G$ a simplicial group. Any group morphism from the Kan loop group~$\Omega X$ to~$G$ is determined by a twisting function~$\tau\colon X\to G$. In 1961, Szczarba gave an explicit construction of a twisting cochain~$t\colon C(X)\to C(G)$ out of a twisting function~$X\to G$. Such a twisting cochain induces a multiplicative map from the cobar construction~$\OM\,C(X)$ to~$C(G)$.

Recently I proved that the map induced by Szczarba's twisting cochain is also comultiplicative; the coproduct on~$\OM\,C(X)$ is defined in terms of homotopy Gerstenhaber operations on~$X$. Shortly afterwards, Minichiello--Rivera--Zeinalian gave a conceptual explanation of this fact, based on the idea of triangulating the cubical cobar construction of~$X$. In this talk I want to elucidate the properties of Szczarba's twisting cochain that make this construction possible.