 The second, quite different line of response to Hellman’s objections is represented in Awodey (2004; cf. Landry 1999). In that article, Awodey outlines a category-theoretic form of structuralism that is decidedly anti-foundationalist.  He holds, in agreement with Hellman and McLarty, that both the Eilenberg-Mac Lane axioms for category theory and the axioms of general topos theory are schematic. But he then argues that category theory in general does not, and should not be taken to, provide a foundation for mathematics, either in a logical or ontological sense. Rather, it presents a general and unifying framework or language for structural mathematics.  He thus rejects Hellman’s assumption that the success of categorical structuralism is in any form dependent on whether category theory is usable as a foundational enterprise or not.