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## 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 n-by-n matrices for n ≥ 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.

Original language | English |
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Pages (from-to) | 457-474 |

Number of pages | 19 |

Journal | Theory and Applications of Categories |

Volume | 29 |

Issue number | 17 |

Publication status | Published - 14 Aug 2014 |

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## Projects

- 1 Finished