On Internal Structure, Categorical Structure, and Representation.

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 (2019 a) has presented an apparent counterexample to this claim; in this note, I argue that the counterexample fails. [ABSTRACT FROM AUTHOR]