Globular set

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 $$X_0, X_1, X_2, \dots$$ equipped with pairs of functions $$s_n, t_n: X_n \to X_{n-1}$$ such that (Equivalently, it is a presheaf on the category of “globes”.) The letters "s", "t" stand for "source" and "target" and one imagines $$X_n$$ consists of directed edges at level n.
 * $$s_n \circ s_{n+1} = s_n \circ t_{n+1},$$
 * $$t_n \circ s_{n+1} = t_n \circ t_{n+1}.$$

A variant of the notion was used by Grothendieck to introduce the notion of an ∞-groupoid. Extending Grothendieck's work, gave a definition of a weak ∞-category in terms of globular sets.