Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Sober topological spaces valued in a quantale   The notion of sobriety is extended to the realm of topological spaces valued
in a commutative and unital quantale, via an adjunction between a category of
quantale modules and the category of quantale-valued topological spaces.
Relations between such sober spaces and quantale-valued domains based on flat
ideals are investigated.

31
The categories of this paper are: ao-sci
35
The categories of this paper are: mtrl-th
4
The categories of this paper are: cond-mat
33
The categories of this paper are: plasm-ph
29
The categories of this paper are: funct-an
20
The categories of this paper are: acc-phys
9
The categories of this paper are: nlin
21
The categories of this paper are: adap-org
8
The categories of this paper are: hep-ex
19
The categories of this paper are: eess
27
The categories of this paper are: comp-gas
7
The categories of this paper are: hep-th
26
The categories of this paper are: bayes-an
15
The categories of this paper are: nucl-ex
36
The categories of this paper are: cmp-lg
24
The categories of this paper are: dg-ga