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

$s_{n}\circ s_{n+1}=s_{n}\circ t_{n+1},$
$t_{n}\circ s_{n+1}=t_{n}\circ t_{n+1}.$

(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.

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.

References

^ Maltsiniotis, G (13 September 2010). "Grothendieck ∞-groupoids and still another definition of ∞-categories". arXiv:1009.2331 [18D05, 18G55, 55P15, 55Q05 18C10, 18D05, 18G55, 55P15, 55Q05].

External links

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

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[1] Maltsiniotis, G (13 September 2010). "Grothendieck ∞-groupoids and still another definition of ∞-categories". arXiv:1009.2331 [18D05, 18G55, 55P15, 55Q05 18C10, 18D05, 18G55, 55P15, 55Q05].

[1]

Globular set

References

Further reading

External links