nLab globe category

The 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.
M. Roy has studied levels in the topos of reflexive globular sets? in the context of F. W. Lawvere‘s concept of Aufhebung (cf. Kennett-Riehl-Roy-Zaks(2011)).

C. Kennett, E. Riehl, M. Roy, M. Zaks, Levels in the toposes of simplicial sets and cubical sets , JPAA 215 no.5 (2011) pp.949-961. (preprint)

category: category

Last revised on December 27, 2014 at 15:14:55. See the history of this page for a list of all contributions to it.