nLab n-quasicategory

Idea

Where a quasicategory is a model for the notion of (infinity,1)-category so an $n$-quasicategory is a model for the notion of (infinity,n)-category for all $n \in \mathbb{N}$.

A definition in terms of cellular sets had originally been suggested by André Joyal. This has then been made to work in terms of a model structure on cellular sets (see there for more details) in (Ara 12).

Related concepts

• Theta-space

References

• Dimitri Ara, Higher quasi-categories vs higher Rezk spaces (arXiv:1206.4354)

A survey is in

• Dimitri AraOn higher quasicategories, 2013 (pdf)