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Generalized Persistence Diagrams

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Generalized Persistence Diagrams
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18
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CC Attribution - NonCommercial - NoDerivatives 4.0 International:
You are free to use, copy, distribute and transmit the work or content in unchanged form for any legal and non-commercial purpose as long as the work is attributed to the author in the manner specified by the author or licensor.
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Abstract
I will interpret the persistence diagram of Cohen-Steiner, Edelsbrunner, and Harer as the Möbius inversion of the rank function. I will then show how to generalize the persistence diagram to the setting of constructible persistence modules valued in any small symmetric monoidal category.