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We define a simple, explicit map sending a morphism $f:M \rightarrow N$ of pointwise finite dimensional persistence modules to a matching between the barcodes of $M$ and $N$.
Corrections and supplementaries to my paper concerning Krull–Remak–Schmidt’s theorem
G. Azumaya · 1950
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Computing persistent homology
A. Zomorodian and G. Carlsson · 2005
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Stability of persistence diagrams
D. Cohen-Steiner, H. Edelsbrunner, and J. Harer · 2007
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Extending persistence using Poincaré and Lefschetz duality
D. Cohen-Steiner, H. Edelsbrunner, and J. Harer · 2008
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Zigzag persistent homology and real-valued functions
G. Carlsson, V. de Silva, and D. Morozov · 2009
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Computational Topology. An Introduction
H. Edelsbrunner and J. Harer · 2010
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Scalar field analysis over point cloud data
F. Chazal, L. Guibas, S. Oudot, and P. Skraba · 2011
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Dualities in persistent (co)homology
V. de Silva, D. Morozov, and M. Vejdemo-Johansson · 2011
Cited alongside, same era.
Proximity of persistence modules
D. Müllner and G. Troianowski · 2011
Cited alongside, same era.
The structure and stability of persistence modules
F. Chazal, V. de Silva, M. Glisse, and S. Oudot · 2012
Cited alongside, same era.
Decomposition of pointwise finite-dimensional persistence modules
W. Crawley-Boevey · 2012
Cited alongside, same era.
Multidimensional Interleavings and Applications to Topological Inference
M. Lesnick · 2012
Cited alongside, same era.
Categorification of persistent homology
P. Bubenik and J. A. Scott · 2014
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Topological pattern recognition for point cloud data
G. Carlsson · 2014
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The persistent homology of a self-map
H. Edelsbrunner, G. Jabłoński, and M. Mrozek · 2014
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Confidence sets for persistence diagrams
B. T. Fasy, F. Lecci, A. Rinaldo, L. Wasserman, S. Balakrishnan, and A. Singh · 2014
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The theory of the interleaving distance on multidimensional persistence modules
M. Lesnick · 2015
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Persistence modules: Algebra and algorithms
P. Skraba and M. Vejdemo-Johansson · 2015
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F. Chazal, L. J. Guibas, S. Y. Oudot, and P. Skraba · 2013
Cited alongside, same era.
Geometry in the space of persistence modules
V. de Silva and V. Nanda · 2013
Cited alongside, same era.
Persistence diagrams are really diagrams
U. Bauer and M. Lesnick
Cited in the paper.
Universality of the homotopy interleaving distance
A. Blumberg and M. Lesnick
Cited in the paper.
Proximity of persistence modules and their diagrams
F. Chazal, D. C. Steiner, M. Glisse, L. J. Guibas, and S. Y. Oudot
Cited in the paper.
Gromov–Hausdorff stable signatures for shapes using persistence
F. Chazal, D. C. Steiner, L. J. Guibas, F. Mémoli, and S. Y. Oudot
Cited in the paper.
The observable structure of persistence modules
F. Chazal, W. Crawley-Boevey, and V. de Silva
Cited in the paper.
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