New Foundations - Cartesian Closure

Cartesian Closure

Unfortunately, the category whose objects are the sets of NF and whose morphisms are the functions between those sets is not cartesian closed; this is a highly desirable property for any set theory to have. Intuitively, it means that the functions of NF do not curry as one would normally expect functions to. Furthermore, it means that NF is not a topos.

Read more about this topic:  New Foundations