 The second argument against the autonomy of categorical foundations has been called the “mismatch objection”.  It concerns the general status of category theory or topos theory; and it is based on the distinction between two ways of understanding mathematical axioms, namely as “structural”, “algebraic”, “schematic” or “Hilbertian”, on the one hand, and as “assertoric” or “Fregean”, on the other hand. As Hellman argues, foundational systems such as classical set theory need to be assertoric in character, in the sense that their axioms describe a comprehensive universe of objects used for the codification of other mathematical structures. Zermelo-Fraenkel set theory is an assertoric, “contentual” theory in this sense. Its axioms (e.g., the power set axiom or the axiom of choice) make general existence claims regarding the objects in the universe of sets.