(∞, n)-category

In mathematics, especially category theory, an (∞, n)-category is a generalization of an ∞-category, where each k-morphism is invertible for $k>n$. Thus, an ∞-category is an (∞, 1)-category, while an ∞-groupoid is an (∞, 0)-category.

See also

• Joyal's theta category

References

• nlab, (infinity,n)-category in nLab
• Loubaton, Félix (2024). "Categorical Theory of $(\infty,ω)$-Categories". arXiv:2406.05425 [math.CT].

Further reading

• (∞,n)-category in Japanese