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Extending obstructions to noncommutative functorial spectra
Theory and applications of categories, Tome 29 (2014), pp. 457-474 Cet article a éte moissonné depuis la source Theory and Applications of Categories website

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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.

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Classification : 16B50, 46L85
Keywords: Ring spectra, Kochen-Specker Theorem 
@article{TAC_2014_29_a16,
     author = {Benno van den Berg and Chris Heunen},
     title = {Extending obstructions to noncommutative functorial spectra},
     journal = {Theory and applications of categories},
     pages = {457--474},
     year = {2014},
     volume = {29},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/TAC_2014_29_a16/}
}
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Benno van den Berg; Chris Heunen. Extending obstructions to noncommutative functorial spectra. Theory and applications of categories, Tome 29 (2014), pp. 457-474. http://geodesic.mathdoc.fr/item/TAC_2014_29_a16/