Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Metrics for generalized persistence modules   We consider the question of defining interleaving metrics on generalized
persistence modules over arbitrary preordered sets. Our constructions are
functorial, which implies a form of stability for these metrics. We describe a
large class of examples, inverse-image persistence modules, which occur
whenever a topological space is mapped to a metric space. Several standard
theories of persistence and their stability can be described in this framework.
This includes the classical case of sublevelset persistent homology. We
introduce a distinction between `soft' and `hard' stability theorems. While our
treatment is direct and elementary, the approach can be explained abstractly in
terms of monoidal functors.

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The categories of this paper are: ao-sci
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The categories of this paper are: bayes-an
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The categories of this paper are: eess
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The categories of this paper are: hep-lat
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The categories of this paper are: patt-sol
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The categories of this paper are: quant-ph
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The categories of this paper are: q-fin
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The categories of this paper are: stat
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The categories of this paper are: astro-ph
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The categories of this paper are: cond-mat
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The categories of this paper are: adap-org
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The categories of this paper are: nlin
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The categories of this paper are: supr-con
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The categories of this paper are: acc-phys
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The categories of this paper are: comp-gas
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The categories of this paper are: gr-qc