Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: On the endomorphism monoid of a profinite semigroup   Necessary and sufficient conditions are given for the endomorphism monoid of
a profinite semigroup to be profinite. A similar result is established for the
automorphism group.

13
The categories of this paper are: quant-ph
1
The categories of this paper are: cs
22
The categories of this paper are: chao-dyn
4
The categories of this paper are: cond-mat
26
The categories of this paper are: bayes-an
28
The categories of this paper are: alg-geom
24
The categories of this paper are: dg-ga
19
The categories of this paper are: eess
3
The categories of this paper are: physics
30
The categories of this paper are: q-alg
8
The categories of this paper are: hep-ex
25
The categories of this paper are: patt-sol
20
The categories of this paper are: acc-phys
16
The categories of this paper are: stat
12
The categories of this paper are: nucl-th
33
The categories of this paper are: plasm-ph