No, I would not say that there exists something in common between those. Cardinality is an emergent property of a set, but that doesn't mean that cardinality exists on its own.
Did Plato ever make the argument that because his Shapes have corners, edges and angles, that therefore corners, edges and angles exist in the same way as the Shapes? I don't recall if he ever described Shapes in those terms.
Did Plato ever make the argument that because his Shapes have corners, edges and angles, that therefore corners, edges and angles exist in the same way as the Shapes? I don't recall if he ever described Shapes in those terms.