There are numerous set theories that allow “set of all sets”, the most well-known of which is probably New Foundations (NF). There are also some theories such as Morse-Kelley theory that have both classes and sets, and include a class of all sets.
There are numerous set theories that allow “set of all sets”, the most well-known of which is probably New Foundations (NF).
The category of sets in NF is not cartesian closed. It’s a non-starter.
There are also some theories such as Morse-Kelley theory that have both classes and sets, and include a class of all sets.
This lacks functor categories e.g. Set^Set.
There are numerous set theories that allow “set of all sets”, the most well-known of which is probably New Foundations (NF). There are also some theories such as Morse-Kelley theory that have both classes and sets, and include a class of all sets.
The category of sets in NF is not cartesian closed. It’s a non-starter.
This lacks functor categories e.g. Set^Set.