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Any functor from the category of C*-algebras to the category of locales that assigns to each commutative C*-algebra its Gelfand spectrum must be trivial on algebras of nxn-matrices for n at least 3. The same obstruction applies to the Zariski, Stone, and Pierce spectra. The possibility of spectra in categories other than that of locales is briefly discussed.
|Title of host publication||Proceedings 8th International Workshop on Quantum Physics and Logic|
|Number of pages||5|
|Publication status||Published - 2012|
|Name||Electronic Proceedings in Theoretical Computer Science|