Extending obstructions to noncommutative functorial spectra
Category Theory
2014-08-20 v1 Rings and Algebras
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. 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.
Cite
@article{arxiv.1407.2745,
title = {Extending obstructions to noncommutative functorial spectra},
author = {Benno van den Berg and Chris Heunen},
journal= {arXiv preprint arXiv:1407.2745},
year = {2014}
}