Noncommutative tensor triangular geometry: classification via Noetherian spectra

Given a monoidal triangulated category T with Noetherian spectrum, we show that there is an order-preserving bijection between the collection of all Thomason subsets of the noncommutative spectrum of T and the collection of all thick two-sided semiprime ideals of T and that it is universal among all such spaces classifying the ideals in question.