# Homotopy Type Theory spheres

## Idea

Spheres can be thought of as a space generated by a point and a (higher-)path constructor. This does not mean their homotopical information is simple however. In face it is very much still an open problem to determine the homotopy groups of spheres.

## Definition

The $n$-sphere can be defined as the suspension of the $(n-1)$-sphere or the iterated suspension of $S^0 := \mathbf{2}$. (a.k.a $\text{Bool}$).

$S^n := \Sigma^n S^0$