An D548: Ordered pair $G_Z = (Z, \mathcal{E}_Z)$ is a tensor product of $G_X$ and $G_Y$ if and only if
(1) | $Z = X \times Y$ (D326: Cartesian product) |
(2) | $\mathcal{E}_Z = \{ x y = (x_1, x_2)(y_1, y_2) : x_1 y_1 \in \mathcal{E}_X \text{ and } x_2 y_2 \in \mathcal{E}_Y \}$ |