Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Non-existing and ill-behaved coequalizers of locally ordered spaces   Categories of locally ordered spaces are especially well-adapted to the
realization of most precubical sets, though their colimits are not so easy to
determine (in comparison with colimits in the category of d-spaces for
example). We use the plural here, as the notion of a locally ordered space vary
from an author to another, only differing according to seemingly anodyne
technical details. As we explain in this article, these differences have
dramatic consequences on colimits. In particular, we show that most categories
of locally ordered spaces are not cocomplete, thus answering a question that
was neglected so far. The strategy is the following: given a directed loop
{\gamma} on a locally ordered space X, we try to identify the image of {\gamma}
with a single point. If it were taken in the category of d-spaces, such an
identification would be likely to create a vortex, while locally ordered spaces
have no vortices. Concretely, the antisymmetry of local orders gets more points
to be identified than in a mere topological quotient. However, the effect of
this phenomenon is in some sense limited to the neighbourhood of (the image of)
{\gamma}. So the existence and the nature of the corresponding coequalizer
strongly depends on the topology around the image of {\gamma}. As an extreme
example, if the latter forms a connected component, the coequalizer exists and
its underlying space matches with the topological coequalizer.

26
The categories of this paper are: bayes-an
29
The categories of this paper are: funct-an
23
The categories of this paper are: solv-int
9
The categories of this paper are: nlin
21
The categories of this paper are: adap-org
22
The categories of this paper are: chao-dyn
27
The categories of this paper are: comp-gas
28
The categories of this paper are: alg-geom
30
The categories of this paper are: q-alg
0
The categories of this paper are: hep-ph
5
The categories of this paper are: gr-qc
32
The categories of this paper are: atom-ph
34
The categories of this paper are: chem-ph
25
The categories of this paper are: patt-sol
7
The categories of this paper are: hep-th
31
The categories of this paper are: ao-sci