 In fact, according to Awodey the central motivation for a category-theoretic approach to mathematics is to sidestep foundational issues concerning the nature of mathematical objects or the study of a single comprehensive universe in which all structures can be represented. While topos theory, say, might well serve as a structural foundation for mathematics, for Awodey such a foundational approach runs against the structuralist perspective embodied in category-theory. In his own words, “the idea of ‘doing mathematics categorically’ involves a different point of view from the customary foundational one” (Awodey 2004: 55). In light of such fundamental, ongoing debates about categorical foundations for mathematics, what are the implications for categorical structuralism in the philosophical sense, along Awodey’s lines and more generally?  This is what we turn to next.