Nlab introduces the [globular category](https://ncatlab.org/nlab/show/globe) as a geometrical model to construct certain higher categorical structures (e. g. strict $\omega$-categories), just as quasi-categories, for example, are modelled on simplices. However, I didn't find much information on the geometric intuition behind their definition.


So, what do these globes really look like? More precisely, how is the geometric realization of globular sets obtained?



What do globes (used to construct globular sets, $\omega$-categories, etc.) actually look like?
The paper on the fundamental [globular groupoid](http://groupoids.org.uk/pdffiles/globularhha.pdf) of a filtered space has some pictures, and a definition of the simplicial nerve of a globular $\omega$-groupoid. Relations with other areas are in the paper M. Kapranov, "Membranes and higher groupoids" arxiv 1602.06166 . My own philosophy is spelled out in this [Aveiro](http://groupoids.org.uk/pdffiles/aveiro-beamer-handout.pdf) presentation. 


See also [this discussion](https://groups.google.com/forum/#!topic/sci.physics.research/8bB-vl66LBI). 


