Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Quantising on a category   We review the problem of finding a general framework within which one can
construct quantum theories of non-standard models for space, or space-time. The
starting point is the observation that entities of this type can typically be
regarded as objects in a category whose arrows are structure-preserving maps.
This motivates investigating the general problem of quantising a system whose
`configuration space' (or history-theory analogue) is the set of objects
$\Ob\Q$ in a category $\Q$.
  We develop a scheme based on constructing an analogue of the group that is
used in the canonical quantisation of a system whose configuration space is a
manifold $Q\simeq G/H$, where $G$ and $H$ are Lie groups. In particular, we
choose as the analogue of $G$ the monoid of `arrow fields' on $\Q$. Physically,
this means that an arrow between two objects in the category is viewed as an
analogue of momentum. After finding the `category quantisation monoid', we show
how suitable representations can be constructed using a bundle (or, more
precisely, presheaf) of Hilbert spaces over $\Ob\Q$. For the example of a
category of finite sets, we construct an explicit representation structure of
this type.

27
The categories of this paper are: comp-gas
25
The categories of this paper are: patt-sol
7
The categories of this paper are: hep-th
30
The categories of this paper are: q-alg
33
The categories of this paper are: plasm-ph
3
The categories of this paper are: physics
4
The categories of this paper are: cond-mat
17
The categories of this paper are: q-fin
21
The categories of this paper are: adap-org
2
The categories of this paper are: math
20
The categories of this paper are: acc-phys
36
The categories of this paper are: cmp-lg
29
The categories of this paper are: funct-an
32
The categories of this paper are: atom-ph
10
The categories of this paper are: q-bio
9
The categories of this paper are: nlin