Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: A new characterisation of groups amongst monoids   We prove that a monoid $M$ is a group if and only if, in the category of
monoids, all points over $M$ are strong. This sharpens and greatly simplifies a
result of Montoli, Rodelo and Van der Linden which characterises groups amongst
monoids as the protomodular objects.

14
The categories of this paper are: math-ph
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The categories of this paper are: eess
20
The categories of this paper are: acc-phys
16
The categories of this paper are: stat
4
The categories of this paper are: cond-mat
37
The categories of this paper are: supr-con
17
The categories of this paper are: q-fin
21
The categories of this paper are: adap-org
3
The categories of this paper are: physics
31
The categories of this paper are: ao-sci
34
The categories of this paper are: chem-ph
28
The categories of this paper are: alg-geom
26
The categories of this paper are: bayes-an
35
The categories of this paper are: mtrl-th
29
The categories of this paper are: funct-an
36
The categories of this paper are: cmp-lg