#
Homotopy Type Theory

suspension (Rev #3)

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

### 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

Revision on September 4, 2018 at 05:17:51 by
Ali Caglayan.
See the history of this page for a list of all contributions to it.