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 AA is the higher inductive type ΣA\Sigma A with the following generators

  • A point N:ΣA\mathrm{N} : \Sigma A
  • A point S:ΣA\mathrm{S} : \Sigma A
  • A function merid:A(N= ΣAS)\mathrm{merid} : A \to (N =_{\Sigma A} S)

Def 2

The suspension of a type AA is a the pushout of 1A1\mathbf 1 \leftarrow A \rightarrow \mathbf 1.

These two definitions are equivalent.

References

category: homotopy theory

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.