Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Completeness of dagger-categories and the complex numbers   The complex numbers are an important part of quantum theory, but are
difficult to motivate from a theoretical perspective. We describe a simple
formal framework for theories of physics, and show that if a theory of physics
presented in this manner satisfies certain completeness properties, then it
necessarily includes the complex numbers as a mathematical ingredient. Central
to our approach are the techniques of category theory, and we introduce a new
category-theoretical tool, called the dagger-limit, which governs the way in
which systems can be combined to form larger systems. These dagger-limits can
be used to characterize the dagger-functor on the category of
finite-dimensional Hilbert spaces, and so can be used as an equivalent
definition of the inner product. One of our main results is that in a
nontrivial monoidal dagger-category with all finite dagger-limits and a simple
tensor unit, the semiring of scalars embeds into an involutive field of
characteristic 0 and orderable fixed field.

30
The categories of this paper are: q-alg
35
The categories of this paper are: mtrl-th
9
The categories of this paper are: nlin
24
The categories of this paper are: dg-ga
0
The categories of this paper are: hep-ph
18
The categories of this paper are: econ
28
The categories of this paper are: alg-geom
16
The categories of this paper are: stat
5
The categories of this paper are: gr-qc
29
The categories of this paper are: funct-an
4
The categories of this paper are: cond-mat
20
The categories of this paper are: acc-phys
36
The categories of this paper are: cmp-lg
15
The categories of this paper are: nucl-ex
33
The categories of this paper are: plasm-ph
19
The categories of this paper are: eess