nLab universal class

 Idea

In class theory, a universal class is a “class of all sets”.

 Definition

In material class theory

to be defined…

In structural class theory

A universal class is a class $U$ such that for all classes $C$, there is a monic class map $U \hookrightarrow C$.

There should also be a definition from a hypothetical “division allegory with class structure” rather than a category with class structure.

See also

• class theory

• category with class structure

• universe

References

• Steve Awodey. Notes on algebraic set theory, Notes for lectures given at the Summer School on Topos Theory, Haute-Bodeux, Belgium. May 29 to June 5, 2005. Carnegie Mellon University Technical Report No. CMU-PHIL-170. June 2005. (pdf)