Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Duality for distributive space   The main source of inspiration for the present paper is the work of R.
Rosebrugh and R.J. Wood on constructive complete distributive lattices where
the authors employ elegantly the concepts of adjunction and module in their
study of ordered sets. Both notions (suitably adapted) are available in
topology too, which permits us to investigate topological, metric and other
kinds of spaces in a similar spirit. Therefore, relative to a choice $\Phi$ of
modules, we consider spaces which admit all colimits with weight in $\Phi$, as
well as (suitably defined) $\Phi$-distributive and $\Phi$-algebraic spaces. We
show that the category of $\Phi$-distributive spaces and $\Phi$-colimit
preserving maps is dually equivalent to the idempotent splitting completion of
a category of spaces and convergence relations between them. We explain the
connection of these results to the traditional duality of spaces with frames,
and conclude further duality theorems. Finally, we study properties and
structures of the resulting categories, in particular monoidal (closed)
structures.

13
The categories of this paper are: quant-ph
34
The categories of this paper are: chem-ph
6
The categories of this paper are: astro-ph
8
The categories of this paper are: hep-ex
20
The categories of this paper are: acc-phys
14
The categories of this paper are: math-ph
25
The categories of this paper are: patt-sol
24
The categories of this paper are: dg-ga
11
The categories of this paper are: hep-lat
35
The categories of this paper are: mtrl-th
23
The categories of this paper are: solv-int
7
The categories of this paper are: hep-th
18
The categories of this paper are: econ
16
The categories of this paper are: stat
1
The categories of this paper are: cs
37
The categories of this paper are: supr-con