Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: The Representation Theorem of Persistent Homology Revisited and
  Generalized   The Representation Theorem by Zomorodian and Carlsson has been the starting
point of the study of persistent homology under the lens of algebraic
representation theory. In this work, we give a more accurate statement of the
original theorem and provide a complete and self-contained proof. Furthermore,
we generalize the statement from the case of linear sequences of $R$-modules to
$R$-modules indexed over more general monoids. This generalization subsumes the
Representation Theorem of multidimensional persistence as a special case.

23
The categories of this paper are: solv-int
15
The categories of this paper are: nucl-ex
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The categories of this paper are: dg-ga
21
The categories of this paper are: adap-org
19
The categories of this paper are: eess
1
The categories of this paper are: cs
11
The categories of this paper are: hep-lat
14
The categories of this paper are: math-ph
35
The categories of this paper are: mtrl-th
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The categories of this paper are: q-fin
7
The categories of this paper are: hep-th
28
The categories of this paper are: alg-geom
4
The categories of this paper are: cond-mat
30
The categories of this paper are: q-alg
12
The categories of this paper are: nucl-th
3
The categories of this paper are: physics