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No-go theorems for functorial localic spectra of noncommutative rings

Author(s): Benno van den Berg | Chris Heunen

Journal: Electronic Proceedings in Theoretical Computer Science
ISSN 2075-2180

Volume: 95;
Issue: Proc. QPL 2011;
Start page: 21;
Date: 2012;
Original page

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.
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