 A second advantage of category theory over set theory, also mentioned in Awodey (1996), is that the categorical notion of structure is “syntax invariant”.  That is to say, unlike in standard model theory the categorical specification of objects in terms of their mapping properties is independent of the choice of a particular signature used for their description (a choice of basic relations, functions, and distinguished elements). Third and most importantly, characteristic for category theory is its focus on morphisms and transformations between mathematical objects that preserve (some of) their internal structure. It is the emphasis on structure-preserving mappings in the specification of objects that is often viewed as a central feature of the structuralist turn in modern mathematics. As such, it was present in various parts of nineteenth- and early twentieth-century mathematics, including Galois theory, Klein’s Erlangen program, Dedekind’s foundational writings, as well as in work on abstract algebra by the Noether school (cf. again Reck &amp; Schiemer forthcoming).