The Clowder Project

Here are some examples of smash products of pointed sets.

1. Smashing With $\text{pt}$. For any pointed set $X$, we have isomorphisms of pointed sets
   \begin{align*} \text{pt}\wedge X & \cong \text{pt},\\ X\wedge \text{pt}& \cong \text{pt}. \end{align*}
2. Smashing With $S^{0}$. For any pointed set $X$, we have isomorphisms of pointed sets
   \begin{align*} S^{0}\wedge X & \cong X,\\ X\wedge S^{0} & \cong X. \end{align*}