Globular set explained

In category theory, a branch of mathematics, a globular set is a higher-dimensional generalization of a directed graph. Precisely, it is a sequence of sets

equipped with pairs of functions such that (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,^[1] gave a definition of a weak ∞-category in terms of globular sets.

Further reading

• Dimitri Ara. On the homotopy theory of Grothendieck ∞ -groupoids. J. Pure Appl. Algebra, 217(7):1237–1278, 2013, arXiv:1206.2941 .

External links

• https://ncatlab.org/nlab/show/globular+set

Notes and References

1. Maltsiniotis . G . Grothendieck ∞-groupoids and still another definition of ∞-categories . 18C10, 18D05, 18G55, 55P15, 55Q05 . 13 September 2010 . 1009.2331 .