#
Homotopy Type Theory

H-space (Rev #3)

# 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 $A$,
- A basepoint $e:A$
- A binary operation $\mu : A \to A \to A$
- for every $a:A$, equalities $\mu(e,a)=a$ and $\mu(a,e)=a$

## Properties

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

## References

HoTT book

Revision on September 4, 2018 at 05:26:35 by
Ali Caglayan.
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