No-go theorems for functorial localic spectra of noncommutative rings
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Publication date
2011-10-27
Authors
Van Den Berg, Benno
Heunen, C.
Editors
Jacobs, Bart
Selinger, Peter
Spitters, Bas
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Part of book
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Abstract
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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van den Berg, B & Heunen, C 2011, No-go theorems for functorial localic spectra of noncommutative rings. in B Jacobs, P Selinger & B Spitters (eds), Proceedings 8th International Workshop on Quantum Physics and Logic (QPL 2011). pp. 21-27. https://doi.org/10.4204/EPTCS.95.3