(∞, n)-category

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

• Joyal's theta category

• Loubaton, Félix (2024). "Categorical Theory of (∞,ω)-Categories". arXiv:2406.05425 [math.CT].
• Simpson, Carlos (2011). Homotopy Theory of Higher Categories. arXiv:1001.4071. doi:10.1017/CBO9780511978111. ISBN 978-0-521-51695-2.
• Barwick, Clark; Schommer-Pries, Christopher (2011). "On the Unicity of the Homotopy Theory of Higher Categories". arXiv:1112.0040 [math.AT].
• Lurie, Jacob (2009). "On the Classification of Topological Field Theories". Current Developments in Mathematics. 2008: 129–280. arXiv:0905.0465. doi:10.4310/CDM.2008.v2008.n1.a3.

• "(infinity,n)-category". ncatlab.org.
• (∞,n)-category in Japanese