Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Variants of epigroups and primary conjugacy   In a semigroup $S$ with fixed $c\in S$, one can construct a new semigroup
$(S,\cdot_c)$ called a \emph{variant} by defining $x\cdot_c y:=xcy$. Elements
$a,b\in S$ are \emph{primarily conjugate} if there exist $x,y\in S^1$ such that
$a=xy, b=yx$. This coincides with the usual conjugacy in groups, but is not
transitive in general semigroups. Ara\'{u}jo \emph{et al.} proved that
transitivity holds in a variety $\mathcal{W}$ of epigroups containing all
completely regular semigroups and their variants, and asked if transitivity
holds for all variants of semigroups in $\mathcal{W}$. We answer this
affirmatively as part of a study of varieties and variants of epigroups.

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The categories of this paper are: hep-ph
16
The categories of this paper are: stat
37
The categories of this paper are: supr-con
24
The categories of this paper are: dg-ga
34
The categories of this paper are: chem-ph
33
The categories of this paper are: plasm-ph
3
The categories of this paper are: physics
35
The categories of this paper are: mtrl-th
32
The categories of this paper are: atom-ph
8
The categories of this paper are: hep-ex
1
The categories of this paper are: cs
31
The categories of this paper are: ao-sci
21
The categories of this paper are: adap-org
12
The categories of this paper are: nucl-th
29
The categories of this paper are: funct-an
28
The categories of this paper are: alg-geom