Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Two applications of monoid actions to cross-sections   Using a construction that builds a monoid from a monoid action, this paper
exhibits an example of a direct product of monoids that admits a prefix-closed
regular cross-section, but one of whose factors does not admit a regular
cross-section; this answers negatively an open question from the theory of
Markov monoids. The same construction is then used to show that for any full
trios $\mathfrak{C}$ and $\mathfrak{D}$ such that $\mathfrak{C}$ is not a
subclass of $\mathfrak{D}$, there is a monoid with a cross-section in
$\mathfrak{C}$ but no cross-section in $\mathfrak{D}$.

20
The categories of this paper are: acc-phys
28
The categories of this paper are: alg-geom
34
The categories of this paper are: chem-ph
4
The categories of this paper are: cond-mat
5
The categories of this paper are: gr-qc
0
The categories of this paper are: hep-ph
30
The categories of this paper are: q-alg
6
The categories of this paper are: astro-ph
1
The categories of this paper are: cs
10
The categories of this paper are: q-bio
24
The categories of this paper are: dg-ga
14
The categories of this paper are: math-ph
23
The categories of this paper are: solv-int
18
The categories of this paper are: econ
3
The categories of this paper are: physics
26
The categories of this paper are: bayes-an