In a 2-category $\mathbb K$, we call strong exact square (resp., absolute exact square) a square $\vf : S \xto[U]{T} V$ such that for every $X\in \mathbb K_0$, the square $\mathbb K[X,\vf]$ is exact in $\Cat$ (resp., for every functor $\Phi : \mathbb K \to \mathbb L$, the square $\Phi(\vf)$ is exact in $\mathbb L$).