Abstract
In order to better understand and to compare interleavings between persistence modules, we elaborate on the algebraic structure of interleavings in general settings. In particular, we provide a representation-theoretic framework for interleavings, showing that the category of interleavings under a fixed translation is isomorphic to the representation category of what we call a shoelace. Using our framework, we show that any two interleavings of the same pair of persistence modules are themselves interleaved. Furthermore, in the special case of persistence modules over \({{\mathbb {R}}}\), we show that matchings between barcodes correspond to the interval-decomposable interleavings.
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Acknowledgements
Killian Meehan is supported in part by JST CREST Mathematics (15656429). Michio Yoshiwaki was partially supported by Osaka City University Advanced Mathematical Institute (MEXT Joint Usage/Research Center on Mathematics and Theoretical Physics JPMXP0619217849).
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Escolar, E.G., Meehan, K. & Yoshiwaki, M. Interleavings and matchings as representations. AAECC 34, 965–993 (2023). https://doi.org/10.1007/s00200-021-00530-7
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DOI: https://doi.org/10.1007/s00200-021-00530-7