1101.5924 (Benno van den Berg et al.)

No-go theorems for functorial localic spectra of noncommutative rings    [PDF]

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.

View original: http://arxiv.org/abs/1101.5924