 Why might category theory be considered a more adequate framework for a mathematical structuralism than other disciplines, in particular traditional (Cantorian, Zermelo-Fraenkel) set theory? It is helpful to consult Awodey (1996) on this issue. According to him, the Bourbaki notion of structure is a direct result of the modern axiomatic tradition of Dedekind, Hilbert, and the Bourbaki group. This tradition eventually led to a structuralist perspective on mathematics. Yet set theory is not an ideal framework for capturing a structuralist understanding of mathematical objects. To begin with, set theory is closely tied to a model-theoretic conception of mathematical theories, including the view that such theories study their models only “up to isomorphism”. But central to a structuralist point of view is the principle (more on which below) to “identify isomorphic objects”; and this principle is well motivated from a category-theoretic viewpoint, but less so if mathematical objects are represented set-theoretically. 