Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: On Structure of cluster algebras of geometric type, II: Green's
  equivalences and paunched surfaces   Following our previous work [18], we introduce the notions of partial seed
homomorphisms and partial ideal rooted cluster morphisms. Related to the theory
of Green's equivalences, the isomorphism classes of sub-rooted cluster algebras
of a rooted cluster algebra are corresponded one-by-one to the regular
$\mathcal D$-classes of the semigroup consisting of partial seed endomorphisms
of the initial seed. Moreover, for a rooted cluster algebra from a Riemannian
surface, they are also corresponded to the isomorphism classes of the so-called
paunched surfaces.

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The categories of this paper are: chem-ph
19
The categories of this paper are: eess
16
The categories of this paper are: stat
26
The categories of this paper are: bayes-an
14
The categories of this paper are: math-ph
25
The categories of this paper are: patt-sol
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The categories of this paper are: funct-an
23
The categories of this paper are: solv-int
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The categories of this paper are: mtrl-th
18
The categories of this paper are: econ
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The categories of this paper are: ao-sci
3
The categories of this paper are: physics
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The categories of this paper are: q-alg
17
The categories of this paper are: q-fin
7
The categories of this paper are: hep-th
9
The categories of this paper are: nlin