 A second distinctive feature of categorical structuralism, not only for Awodey, concerns a certain “top-down” conception of mathematical objects characteristic for category theory. According to standard set theory, mathematical objects are constructed from the “bottom up”, in successive steps starting from some ground level (the empty set or also a domain of urelements). Every object is thus determined, as a set, in terms of its members. In contrast, mathematical objects in category theory are characterized in a top-down fashion, starting with the Eilenberg-Mac Lane axioms and using the notion of morphism. Hence, the objects in a given category, such as that of rings or topological spaces, are not considered independently of the relevant morphisms. They are fully determined by their mapping properties, as expressible in the language of category theory. Nothing further is assumed about their inner constitution. In particular, questions about their set-theoretic nature are considered redundant (see also Landry &amp; Marquis 2005.)