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Sofia B (Oct 05 2026 at 13:44):I remember vaguely that there are identities built out of +, ×, and exponents that hold between natural numbers but that can't be proved by constructing an isomorphism in a general Cartesian closed category with coproducts, but I can't remember the name or source of this observation
Nathanael Arkor (Oct 05 2026 at 13:52):This is the study of Tarski's high school algebra problem (which was originally formulated as a problem in first order logic, but has also been studied in the categorical context).