 Categorical structuralists typically argue that category theory presents the most adequate framework for a structuralist understanding of mathematical objects given that all the properties expressible in its language turn out to be structural (see, e.g., McLarty 1993, Awodey 2004, and Marquis 2013). This is so because the category-theoretic study of mathematical objects, such as rings or topological spaces, allows us to express just the right kind of “structural information”, namely information about the structural properties of these objects. In this context, structural properties are usually characterized in terms of the notion of isomorphism invariance. Given a category C, a morphism \(f: A \rightarrow B\) presents an isomorphism between objects A and B if and only if there is a morphism \(g: B \rightarrow A\) such that \(g \circ f = 1_A\) and \(f \circ g =1_B\). A property P of an object A in category C is then structural if it remains invariant under the isomorphisms in C, that is, if \(P(A) \leftrightarrow P(f(A))\), for all isomorphisms f (cf. Awodey 1996).