2011/01/31 by Benno van den Berg, Chris Heunen
Mathematics · Physics and Astronomy · #math.RA #math.CT #quant-ph
paper · pdf · doi:10.4204/eptcs.95.3
published as EPTCS 95, 2012, pp. 21-25 · In Proceedings QPL 2011, arXiv:1210.0298
arxiv created 2012/10/02 · arxiv updated 2012/10/03
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.