The Clowder Project

\begin{align*} R_{1} & \colon A\mathrel {\rightarrow \kern -9.5pt\mathrlap {|}\kern 6pt}B,\\ S_{1} & \colon B\mathrel {\rightarrow \kern -9.5pt\mathrlap {|}\kern 6pt}C,\\ R_{2} & \colon X\mathrel {\rightarrow \kern -9.5pt\mathrlap {|}\kern 6pt}Y,\\ S_{2} & \colon Y\mathrel {\rightarrow \kern -9.5pt\mathrlap {|}\kern 6pt}Z \end{align*}

\[ \webleft (S_{1}\mathbin {\diamond }R_{1}\webright )\times \webleft (S_{2}\mathbin {\diamond }R_{2}\webright )=\webleft (S_{1}\times S_{2}\webright )\mathbin {\diamond }\webleft (R_{1}\times R_{2}\webright ). \]