Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Gelfand spectra in Grothendieck toposes using geometric mathematics   In the (covariant) topos approach to quantum theory by Heunen, Landsman and
Spitters, one associates to each unital C*-algebra, A, a topos T(A) of sheaves
on a locale and a commutative C*-algebra, a, within that topos. The Gelfand
spectrum of a is a locale S in this topos, which is equivalent to a bundle over
the base locale. We further develop this external presentation of the locale S,
by noting that the construction of the Gelfand spectrum in a general topos can
be described using geometric logic. As a consequence, the spectrum, seen as a
bundle, is computed fibrewise.
  As a by-product of the geometricity of Gelfand spectra, we find an explicit
external description of the spectrum whenever the topos is a functor category.
As an intermediate result we show that locally perfect maps compose, so that
the externalization of a locally compact locale in a topos of sheaves over a
locally compact locale is locally compact, too.

23
The categories of this paper are: solv-int
13
The categories of this paper are: quant-ph
6
The categories of this paper are: astro-ph
25
The categories of this paper are: patt-sol
7
The categories of this paper are: hep-th
37
The categories of this paper are: supr-con
30
The categories of this paper are: q-alg
4
The categories of this paper are: cond-mat
5
The categories of this paper are: gr-qc
22
The categories of this paper are: chao-dyn
18
The categories of this paper are: econ
26
The categories of this paper are: bayes-an
19
The categories of this paper are: eess
15
The categories of this paper are: nucl-ex
31
The categories of this paper are: ao-sci
10
The categories of this paper are: q-bio