Homotopy Type Theory
smash product

Idea

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

1ABA×B\mathbf 1 \leftarrow A \wedge B \rightarrow A \times B

where ABA×BA \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 ABA \wedge B and is pointed by ABinl( 1)\star_{A \wedge B}\equiv\mathrm{inl}(\star_{\mathbf 1})

It can also be defined as the pushout of the span

2A+BA×B\mathbf{2} \leftarrow A + B \rightarrow A \times B

Definition

References

category: homotopy theory