nLab locally presentable (infinity,n)-category

Idea

The generalization of the notion of locally presentable categories and locally presentable $(\infty,1)$-categories to $(\infty,n)$-categories.

Related concepts

• (∞,n)-topos

References

• Germán Stefanich: Presentable $(\infty,n)$-categories [arXiv:2011.03035]

• Ko Aoki: Higher presentable categories and limits [arXiv:2510.13503]

In the context of duality between geometry and algebra between higher geometry and higher algebra (“Gestalten”):

• Peter Scholze: Geometry and Higher Category Theory, lecture notes (2026) [webpage, pdf]