  Proponents of category theory long hoped to escape the limits of set theory
by founding mathematics on an unlimited category theory in which large
categories, such as the category Grp of all groups, the category Top of all
topological spaces, and the category Cat of all categories, would be
(first-class) entities rather than just classes. Several proposals were put
forward by Lawvere, MacLane, and Feferman, but none were successful. Feferman,
in 1969 and 2013, proposed three requirements which an axiomatic theory of
categories should fulfull in order to be an "unlimited category theory for
mathematics". But in 2015 Michael Ernst proved that if an axiomatic theory of
categories satisfied Fefermann's three requirements, then it is inconsistent.
This paper, a presentation to the Indiana University, Bloomington, Logic
Seminar, exposits Ernst's paper.
