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

(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.
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