Yes, that is correct. However, Nietzsche assumed that individuals would derive their own rules and ethics from a form of the categorical imperative of strength and dignity.
That's definitely a point where Plato and Nietzsche diverge.
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Nietzsche's Zarathustra is more like a heraklitian Empedokles, dancing his last dance at the edge of the volcano of chaos.... the anti-Platon
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