A Theory of Sub-Barcodes

  title={A Theory of Sub-Barcodes},
  author={Oliver A. Chubet and Kirk P. Gardner and Don Sheehy},
From the work of Bauer and Lesnick, it is known that there is no functor from the category of pointwise finite-dimensional persistence modules to the category of barcodes and overlap matchings . In this work, we introduce sub-barcodes and show that there is a functor from the category of factorizations of persistence module homomorphisms to a poset of barcodes ordered by the sub-barcode relation . Sub-barcodes and factorizations provide a looser alternative to bottleneck matchings and… 

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