That is to say, the smash product of pointed sets is defined so as to induce a bijection between the following data:
- Pointed maps $f\colon X\wedge Y\to Z$.
- Maps of sets $f\colon X\times Y\to Z$ satisfying
\begin{align*} f\webleft (x_{0},y\webright ) & = z_{0},\\ f\webleft (x,y_{0}\webright ) & = z_{0} \end{align*}
for each $x\in X$ and each $y\in Y$.
