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 equipped with pairs of functions such that
The letters "s", "t" stand for "source" and "target" and one imagines consists of directed edges at level n.
In the context of a graph, each dimension is represented as a set of -cells. Vertices would make up the 0-cells, edges connecting vertices would be 1-cells, and then each dimension higher connects groups of the dimension beneath it.
It can be viewed as a specific instance of the polygraph. In a polygraph, a source or target of a -cell may consist of an entire path of elements of -cells, but a globular set restricts this to singular elements of -cells.
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.