# Homotopy Type Theory smash product

## Idea

The smash product of two pointed types $A,B$ can be defined as the pushout of the span

$\mathbf 1 \leftarrow A \wedge B \rightarrow A \times B$

where $A \wedge B \rightarrow A \times B$ is the inclusion of the wedge sum in the product type? both of which are pointed. The resulting pushout is denoted the smash product $A \wedge B$ and is pointed by $\star_{A \wedge B}\equiv\mathrm{inl}(\star_{\mathbf 1})$

It can also be defined as the pushout of the span

$\mathbf{2} \leftarrow A + B \rightarrow A \times B$

## References

category: homotopy theory

Last revised on February 14, 2019 at 03:28:55. See the history of this page for a list of all contributions to it.