Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Configuration spaces and directed paths on the final precubical set   The main goal of this paper is to prove that the space of directed loops on
the final precubical set is homotopy equivalent to the "total" configuration
space of points on the plane; by "total" we mean that any finite number of
points in a configuration is allowed. We also provide several applications: we
define new invariants of precubical sets, prove that directed path spaces on
any precubical complex have the homotopy types of CW-complexes and construct
certain presentations of configuration spaces of points on the plane as nerves
of categories.

16
The categories of this paper are: stat
25
The categories of this paper are: patt-sol
30
The categories of this paper are: q-alg
5
The categories of this paper are: gr-qc
8
The categories of this paper are: hep-ex
11
The categories of this paper are: hep-lat
6
The categories of this paper are: astro-ph
12
The categories of this paper are: nucl-th
22
The categories of this paper are: chao-dyn
33
The categories of this paper are: plasm-ph
10
The categories of this paper are: q-bio
34
The categories of this paper are: chem-ph
32
The categories of this paper are: atom-ph
4
The categories of this paper are: cond-mat
31
The categories of this paper are: ao-sci
3
The categories of this paper are: physics