Higher Interpolation and Extension for Persistence Modules

@article{Bubenik2017HigherIA,
  title={Higher Interpolation and Extension for Persistence Modules},
  author={Peter Bubenik and Vin de Silva and Vidit Nanda},
  journal={SIAM J. Appl. Algebra Geom.},
  year={2017},
  volume={1},
  pages={272-284}
}
The use of topological persistence in contemporary data analysis has provided considerable impetus for investigations into the geometric and functional-analytic structure of the space of persistence modules. In this paper, we isolate a coherence criterion which guarantees the extensibility of non-expansive maps into this space across embeddings of the domain to larger ambient metric spaces. Our coherence criterion is category-theoretic, allowing Kan extensions to provide the desired extensions… 

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