On internal structure, categorical structure, and representation

Abstract

<jats:title>Abstract</jats:title> <jats:p>If categorical equivalence is a good criterion of theoretical equivalence, then it would seem that if some class of mathematical structures is represented as a category, then any other class of structures categorically equivalent to it will have the same representational capacities. [Hudetz, 2019a] has presented an apparent counterexample to this claim; in this note, I argue that the counterexample fails.</jats:p>