globe

- homotopy hypothesis-theorem
- delooping hypothesis-theorem
- periodic table
- stabilization hypothesis-theorem
- exactness hypothesis
- holographic principle

- (n,r)-category
- Theta-space
- ∞-category/∞-category
- (∞,n)-category
- (∞,2)-category
- (∞,1)-category
- (∞,0)-category/∞-groupoid
- n-category = (n,n)-category
- 2-category, (2,1)-category
- 1-category
- 0-category
- (?1)-category?
- (?2)-category?

- n-poset = (n-1,n)-category
- n-groupoid = (n,0)-category

- categorification/decategorification
- geometric definition of higher category
- Kan complex
- quasi-category
- simplicial model for weak ∞-categories?

- algebraic definition of higher category
- stable homotopy theory

The cellular *$n$-globe* is the globular analog of the cellular $n$-simplex. It is one of the basic geometric shapes for higher structures.

The **cellular $n$-globe** $G_n$ is the globular set represented by the object $[n]$ in the globe category $G$:

$G_n := Hom_G(-,[n])
\,.$

The 0-globe is the singleton set, the category with a single morphism.

The 1-globe is the interval category.

The 3-globe looks like this

There is a unique structure of a strict omega-category, an n-category in fact, on the $n$-globe. This makes the collection of $n$-globes arrange themselves into a *co-globular $\omega$-category*, i.e. a functor

$G \to \omega Cat$

$[n] \mapsto G_n
\,.$

The *orientals* translate between simplices and globles.

See the references at *strict omega-category* and at *oriental*.

Last revised on May 17, 2012 at 10:53:26. See the history of this page for a list of all contributions to it.