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Session S27 - Categories and Topology

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Persistence Diagrams as Change Action Derivatives

Deni Salja

Dalhousie , Canada   -   This email address is being protected from spambots. You need JavaScript enabled to view it.

In 2019 McCleary and Patel proposed a generalization of a persistence diagram for a `multi-parameter filtration' of chain complexes of an abelian category as the Möbius inversion of the rank function of the associated `birth-death-(sub)object.' At the 2019 CMS winter meeting Patel spoke at the TDA session about this work and mentioned how he thought of Möbius inversion as a derivative. This poster shows how to (extend and then) view a certain quotient object in their work as a change-action derivative in the sense of Alvarez-Picallo and Lemay.

Joint work with Dr. Kristine Bauer (University of Calgary).

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