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Extending obstructions to noncommutative functorial spectra

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Benno van den Berg and 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 $n$-by-$n$ matrices for $n \geq 3$. This
obstruction also applies to other spectra such as those named after
Zariski, Stone, and Pierce. We extend these no-go results to functors with
values in (ringed) topological spaces, (ringed) toposes, schemes, and
quantales. The possibility of spectra in other categories is discussed.

Keywords:
Ring spectra, Kochen-Specker Theorem

2010 MSC:
16B50, 46L85

*Theory and Applications of Categories,*
Vol. 29, 2014,
No. 17, pp 457-474.

Published 2014-08-14.

http://www.tac.mta.ca/tac/volumes/29/17/29-17.pdf

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