Instruct: Identify the main and secondary category of Arxiv papers based on the titles
Query: Free product of absolute Galois groups   The free profinite product of finitely many absolute Galois group is an
absolute Galois group.

4
The categories of this paper are: cond-mat
16
The categories of this paper are: stat
23
The categories of this paper are: solv-int
24
The categories of this paper are: dg-ga
19
The categories of this paper are: eess
7
The categories of this paper are: hep-th
30
The categories of this paper are: q-alg
28
The categories of this paper are: alg-geom
8
The categories of this paper are: hep-ex
10
The categories of this paper are: q-bio
25
The categories of this paper are: patt-sol
11
The categories of this paper are: hep-lat
32
The categories of this paper are: atom-ph
3
The categories of this paper are: physics
20
The categories of this paper are: acc-phys
35
The categories of this paper are: mtrl-th