Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: A Compactness Theorem for The Dual Gromov-Hausdorff Propinquity   We prove a compactness theorem for the dual Gromov-Hausdorff propinquity as a
noncommutative analogue of the Gromov compactness theorem for the
Gromov-Hausdorff distance. Our theorem is valid for subclasses of quasi-Leibniz
compact quantum metric spaces of the closure of finite dimensional
quasi-Leibniz compact quantum metric spaces for the dual propinquity. While
finding characterizations of this class proves delicate, we show that all
nuclear, quasi-diagonal quasi-Leibniz compact quantum metric spaces are limits
of finite dimensional quasi-Leibniz compact quantum metric spaces. This result
involves a mild extension of the definition of the dual propinquity to
quasi-Leibniz compact quantum metric spaces, which is presented in the first
part of this paper.

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The categories of this paper are: solv-int
3
The categories of this paper are: physics
4
The categories of this paper are: cond-mat
5
The categories of this paper are: gr-qc
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The categories of this paper are: nucl-ex
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The categories of this paper are: adap-org
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The categories of this paper are: dg-ga
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The categories of this paper are: nlin
1
The categories of this paper are: cs
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The categories of this paper are: atom-ph
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The categories of this paper are: plasm-ph
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The categories of this paper are: math-ph
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The categories of this paper are: nucl-th
10
The categories of this paper are: q-bio
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The categories of this paper are: supr-con
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The categories of this paper are: hep-th