(Equivalently, it is a presheaf on the category of “globes”.) The letters "s", "t" stand for "source" and "target" and one imagines consists of directed edges at level n.
A variant of the notion was used by Grothendieck to introduce the notion of an ∞-groupoid. Extending Grothendieck's work, (Maltsiniotis 2010) gave a definition of a weak ∞-category in terms of globular sets.
- Dimitri Ara. On the homotopy theory of Grothendieck ∞ -groupoids. J. Pure Appl. Algebra, 217(7):1237–1278, 2013, arXiv:1206.2941 .
- G. Maltsiniotis. Grothendieck ∞-groupoids and still another definition of ∞-categories, preprint, 2010.