## How to be concrete when you don't have a choice

### David Roberts – 11 May 2022

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.

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