Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Quantum sets   A quantum set is defined to be simply a set of nonzero finite-dimensional
Hilbert spaces. Together with binary relations, essentially the quantum
relations of Weaver, quantum sets form a dagger compact category. Functions
between quantum sets are certain binary relations that can be characterized in
terms of this dagger compact structure, and the resulting category of quantum
sets and functions generalizes the category of ordinary sets and functions in
the manner of noncommutative mathematics. In particular, this category is dual
to a subcategory of von Neumann algebras. The basic properties of quantum sets
are presented thoroughly, with the noncommutative dictionary in mind, and with
an eye to convenient application. As a motivating example, a notion of quantum
graph coloring is derived within this framework, and it is shown to be
equivalent to the notion that appears in the quantum information theory
literature.

5
The categories of this paper are: gr-qc
35
The categories of this paper are: mtrl-th
18
The categories of this paper are: econ
23
The categories of this paper are: solv-int
8
The categories of this paper are: hep-ex
4
The categories of this paper are: cond-mat
20
The categories of this paper are: acc-phys
22
The categories of this paper are: chao-dyn
30
The categories of this paper are: q-alg
7
The categories of this paper are: hep-th
27
The categories of this paper are: comp-gas
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
26
The categories of this paper are: bayes-an
11
The categories of this paper are: hep-lat