No-go theorems for functorial localic spectra of noncommutative rings

Benno van den Berg
Chris Heunen

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.

In Bart Jacobs, Peter Selinger and Bas Spitters: Proceedings 8th International Workshop on Quantum Physics and Logic (QPL 2011), Nijmegen, Netherlands, October 27-29, 2011, Electronic Proceedings in Theoretical Computer Science 95, pp. 21–25.
Published: 1st October 2012.

ArXived at: http://dx.doi.org/10.4204/EPTCS.95.3 bibtex PDF
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