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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 , … {\displaystyle X_{0},X_{1},X_{2},\dots } equipped with pairs of functions s n , t n : X n → X n − 1 {\displaystyle s_{n},t_{n}:X_{n}\to X_{n-1}} such that
The letters "s", "t" stand for "source" and "target" and one imagines X n {\displaystyle X_{n}} 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, gave a definition of a weak ∞-category in terms of globular sets.