In a 2-category $\mathbb{K}$, we call multiplicative square the following data: a square $\vf : S \xto[U]{T} V$ and, for each $R,\Omega, P : R \to X$, $Q : R \to Y$, $F : X \to \Omega$, $G:Y\to \Omega$, $\alpha : UP \To VQ$, $\beta : FS \To GT$, a 2-morphism $\beta\otimes_\vf\alpha : FP \To GQ$ satisfying the conditions

• (un) $\beta\otimes_\vf\vf =\beta$, $\vf\otimes_\vf\alpha=\alpha$ for all $\alpha,\beta$;
• (bil) $(b*\beta) \otimes_\vf (\alpha * a)=b * (\beta\otimes_\vf\alpha) * a$ for every $a : R\tick \to R$, $b : \Omega \to \Omega\tick$.