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. 1
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