In mathematics, n-categories are a high-order generalization of the notion of category. The category of (small) n-categories n-Cat is defined by induction on n by:

• the category 0-Cat is the category Set of sets and functions,
• the category (n+1)-Cat is the category of categories enriched over the category n-Cat (with the monoidal structure induced by the composition).

In particular, the category 1-Cat is the category Cat of small categories and functors.

See also

• 2-category

References

Higher category theory