 The third main part of Dedekind’s approach connects and complements the first two. Not only does he study infinite systems of objects or whole classes of such systems; and not only does he attempt to identify basic concepts applicable to them, especially higher-level concepts. He also tends to do both, often in conjunction, by considering mappings on the systems studied, especially structure-preserving mappings (homomorphisms, isomorphisms, implicitly also category-theoretic functors, etc.). This implies that what is crucial about a mathematical phenomenon may not lie on the surface (concrete features of examples, particular symbolisms, etc.) but go deeper. And while the deeper features are often captured set-theoretically (Dedekind cuts, ideals, quotient structures, etc.), this points beyond set theory in the end, towards category theory, especially in Dedekind’s later works (Corry 2004, McLarty 2006, Ferreirós 2017a, 2017b).