nLab
cartesian closed (infinity,1)-category

Definition

An (∞,1)-category with (∞,1)-products $\times$ which is a closed monoidal (∞,1)-category with respect to $\otimes :=\times$ is called a cartesian closed $(\mathrm{\infty },1)$-category.

Examples

Every (∞,1)-topos is a cartesian closed $(\mathrm{\infty },1)$-category. See the section Closed monoidal structure.

Related concepts

• cartesian closed category, locally cartesian closed category

• cartesian closed functor, locally cartesian closed functor

• cartesian closed model category, locally cartesian closed model category

• cartesian closed (∞,1)-category, locally cartesian closed (∞,1)-category