nLab universal class



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


In material class theory

to be defined…

In structural class theory

A universal class is a class UU such that for all classes CC, there is a monic class map UCU \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


  • 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)

Last revised on December 19, 2022 at 15:18:14. See the history of this page for a list of all contributions to it.