 A natural response to this challenge is to refine the original structuralist thesis, e.g., by saying that abstract structures only have structural properties “essentially”, that only such properties are “constitutive” for them, or something similar, while admitting that they have other properties too (see Reck 2003, Schiemer &amp; Wigglesworth forthcoming). This leads to questions about how exactly to make this distinction. But even if it is taken to constitute a satisfactory response, another problem remains: How can we distinguish “structural” from “non-structural” properties in the first place? Several answers to that question have been proposed in turn, e.g., that structural properties are those definable in a certain way, or that they are those preserved under relevant morphisms.  Yet no consensus on that issue has been reached either (see Korbmacher &amp; Schiemer 2018, also for further references).