No-go theorems for functorial localic spectra of noncommutative rings

B. van den Berg; C. Heunen

doi:10.4204/EPTCS.95.3

No-go theorems for functorial localic spectra of noncommutative rings

B. van den Berg
, C. Heunen

extern

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution › Academic › peer-review

Abstract

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.

Original language	English
Title of host publication	Proceedings 8th International Workshop on Quantum Physics and Logic (QPL 2011)
Editors	Bart Jacobs, Peter Selinger, Bas Spitters
Pages	21-27
Number of pages	7
DOIs	https://doi.org/10.4204/EPTCS.95.3
Publication status	Published - 27 Oct 2011

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Quantum Physics and Logic

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10.4204/EPTCS.95.3

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title = "No-go theorems for functorial localic spectra of noncommutative rings",

abstract = "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.",

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N2 - 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.

AB - 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.

U2 - 10.4204/EPTCS.95.3

DO - 10.4204/EPTCS.95.3

M3 - Conference contribution

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BT - Proceedings 8th International Workshop on Quantum Physics and Logic (QPL 2011)

A2 - Jacobs, Bart

A2 - Selinger, Peter

A2 - Spitters, Bas

ER -

No-go theorems for functorial localic spectra of noncommutative rings

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