Higher category theory
higher category theory
Extra properties and structure
The cellular -globe is the globular analog of the cellular -simplex. It is one of the basic geometric shapes for higher structures.
The cellular -globe is the globular set represented by the object in the globe category :
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 -globe. This makes the collection of -globes arrange themselves into a co-globular -category, i.e. a functor
G \to \omega Cat
[n] \mapsto G_n
Relation to simplices
The orientals translate between simplices and globles.
See the references at strict omega-category and at oriental.