There are a pair of theorems about concrete categories from the early 70s, by Freyd and Kučera, both of which are proved by assuming the axiom of global choice, and well-ordering the class of objects. Kučera's proof even starts by assuming blithely that the objects of the arbitrary starting category *are* ordinals. Martti Karvonen and I have improved these theorems to hold in the choiceless setting, and to work in algebraic set theory (albeit with classical logic) rather than traditional material set theory.