If $\mathbb{K}$ has comma and co-comma objects, the presence of $\firstblank\otimes_\vf \sndblank$ amounts, with $(U\downarrow V)$ a comma object and $(S\diamond T)$ a cocomma object, to a 2-cell $\otimes : i_0 d_0 \To i_1d_1$ such that in such a way that $\beta \otimes_\vf \alpha = \underline\beta * \otimes * \overline\alpha$.

In a category $\mathbb{K}$ (regarded as a 2-category without nontrivial 2-morphisms) we recover the definition of exact square given in Grandis (Grandis, 1977).