#
Homotopy Type Theory

suspension

## Idea

The suspension is the universal way to make points into paths.

## Definitions

### Def 1

The suspension of a type $A$ is the higher inductive type $\Sigma A$ with the following generators

- A point $\mathrm{N} : \Sigma A$
- A point $\mathrm{S} : \Sigma A$
- A function $merid : A \to (\mathrm{N} =_{\Sigma A} \mathrm{S})$

### Def 2

The suspension of a type $A$ is a the pushout of $\mathbf 1 \leftarrow A \rightarrow \mathbf 1$.

These two definitions are equivalent.

## References

Last revised on September 4, 2018 at 05:48:52.
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