Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: On universal objects in the class of graph inverse semigroups   In this paper we show that polycyclic monoids are universal objects in the
class of graph inverse semigroups. In particular, we prove that a graph inverse
semigroup $G(E)$ over a directed graph $E$ embeds into the polycyclic monoid
$\mathcal{P}_{\lambda}$ where $\lambda=|G(E)|$. We show that each graph inverse
semigroup $G(E)$ admits the coarsest inverse semigroup topology $\tau$.
Moreover, each injective homomorphism from $(G(E),\tau)$ to the
$(\mathcal{P}_{|G(E)|},\tau)$ is a topological embedding.

37
The categories of this paper are: supr-con
7
The categories of this paper are: hep-th
12
The categories of this paper are: nucl-th
4
The categories of this paper are: cond-mat
33
The categories of this paper are: plasm-ph
19
The categories of this paper are: eess
17
The categories of this paper are: q-fin
1
The categories of this paper are: cs
16
The categories of this paper are: stat
14
The categories of this paper are: math-ph
31
The categories of this paper are: ao-sci
3
The categories of this paper are: physics
27
The categories of this paper are: comp-gas
29
The categories of this paper are: funct-an
20
The categories of this paper are: acc-phys
10
The categories of this paper are: q-bio