Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Homotopy Theory in Digital Topology   Digital topology is part of the ongoing endeavour to understand and analyze
digitized images. With a view to supporting this endeavour, many notions from
algebraic topology have been introduced into the setting of digital topology.
But some of the most basic notions from homotopy theory remain largely absent
from the digital topology literature. We embark on a development of homotopy
theory in digital topology, and define such fundamental notions as function
spaces, path spaces, and cofibrations in this setting. We establish digital
analogues of basic homotopy-theoretic properties such as the homotopy extension
property for cofibrations, and the homotopy lifting property for certain
evaluation maps that correspond to path fibrations in the topological setting.
We indicate that some depth may be achieved by using these homotopy-theoretic
notions to give a preliminary treatment of Lusternik-Schnirelmann category in
the digital topology setting. This topic provides a connection between digital
topology and critical points of functions on manifolds, as well as other topics
from topological dynamics.

24
The categories of this paper are: dg-ga
17
The categories of this paper are: q-fin
9
The categories of this paper are: nlin
26
The categories of this paper are: bayes-an
14
The categories of this paper are: math-ph
5
The categories of this paper are: gr-qc
33
The categories of this paper are: plasm-ph
34
The categories of this paper are: chem-ph
37
The categories of this paper are: supr-con
13
The categories of this paper are: quant-ph
15
The categories of this paper are: nucl-ex
7
The categories of this paper are: hep-th
27
The categories of this paper are: comp-gas
20
The categories of this paper are: acc-phys
21
The categories of this paper are: adap-org
8
The categories of this paper are: hep-ex