No-go theorems for functorial localic spectra of noncommutative rings

Details No-go theorems for functorial localic spectra of noncommutative rings No-go theorems for functorial localic spectra of noncommutative rings

2011-01-31

arxiv.org/abs/1101.5924v2

Mathematics

Rings and Algebras

5 pages, updated introduction and discussion

Scientific paper

Any functor from the category of C*-algebras to the category of locales which
assigns to each commutative C*-algebra its Gelfand spectrum must be trivial on
algebras of n-by-n matrices for n>=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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