Homotopy Type Theory
H-space (Rev #3, changes)

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Contents

Idea

Classically, an H-space is a homotopy type equipped with the structure of a unital magma in the homotopy category (only).

Definition

A H-Space consists of

  • A type AA,
  • A basepoint e:Ae:A
  • A binary operation μ:AAA\mu : A \to A \to A
  • for every a:Aa:A, equalities μ(e,a)=a\mu(e,a)=a and μ(a,e)=a\mu(a,e)=a

Properties

Let AA be a connected H-space. Then for every a:Aa:A, the maps μ(a,),μ(,a):AA\mu(a,-),\mu(-,a):A \to A are equivalences.

References

HoTT book

Revision on September 4, 2018 at 05:26:35 by Ali Caglayan. See the history of this page for a list of all contributions to it.