nLab locally cartesian closed functor

Definition

A locally cartesian closed functor is a functor between locally cartesian closed categories that preserves the locally cartesian closed structure up to coherent isomorphism.

Examples

• Every logical functor between toposes is locally cartesian closed.
• Every locally connected geometric morphism is locally cartesian closed. (Elephant C3.3.1)

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

References

Elephant C3.3.1