Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Closed inverse subsemigroups of graph inverse semigroups   As part of his study of representations of the polycylic monoids, M.V. Lawson
described all the closed inverse submonoids of a polycyclic monoid $P_n$ and
classified them up to conjugacy. We show that Lawson's description can be
extended to closed inverse subsemigroups of graph inverse semigroups. We then
apply B. Schein's theory of cosets in inverse semigroups to the closed inverse
subsemigroups of graph inverse semigroups: we give necessary and sufficient
conditions for a closed inverse subsemigroup of a graph inverse semigroup to
have finite index, and determine the value of the index when it is finite.

4
The categories of this paper are: cond-mat
5
The categories of this paper are: gr-qc
3
The categories of this paper are: physics
13
The categories of this paper are: quant-ph
15
The categories of this paper are: nucl-ex
19
The categories of this paper are: eess
37
The categories of this paper are: supr-con
26
The categories of this paper are: bayes-an
12
The categories of this paper are: nucl-th
7
The categories of this paper are: hep-th
33
The categories of this paper are: plasm-ph
0
The categories of this paper are: hep-ph
10
The categories of this paper are: q-bio
30
The categories of this paper are: q-alg
32
The categories of this paper are: atom-ph
16
The categories of this paper are: stat