globe category

The **globe category** $G$ encodes one of the main geometric shapes for higher structures. Its objects are the standard cellular $n$-globes, and presheaves on it are globular sets.

It may also be called the globular category, although that term has other interpretations.

The **globe category** $G$ is the category whose objects are the non-negative integers and whose morphisms are generated from

$\sigma_n : [n] \to [n+1]$

$\tau_n : [n] \to [n+1]$

for all $n \in \mathbb{N}$ subject to the relations (dropping obvious subscripts)

$\sigma\circ \sigma = \tau \circ \sigma$

$\sigma\circ \tau = \tau \circ \tau$

If we add the generating morphisms

$\iota_n : [n+1] \to [n]$

subject to the relations

$\iota \circ \sigma = \mathrm{Id}$

$\iota \circ \tau = \mathrm{Id}
\,.$

we obtain the **reflexive globe category**.

- The globe category is used to define globular sets.

category: category

Revised on November 1, 2012 03:16:40
by Urs Schreiber
(82.169.65.155)