Categorification of Persistent Homology

@article{Bubenik2014CategorificationOP,
  title={Categorification of Persistent Homology},
  author={Peter Bubenik and Jonathan A. Scott},
  journal={Discrete \& Computational Geometry},
  year={2014},
  volume={51},
  pages={600-627}
}
We redevelop persistent homology (topological persistence) from a categorical point of view. The main objects of study are $\mathbf {(\mathbb {R},\leq)}$-indexed diagrams in some target category. A set of such diagrams has an interleaving distance, which we show generalizes the previously studied bottleneck distance. To illustrate the utility of this approach, we generalize previous stability results for persistence, extended persistence, and kernel, image, and cokernel persistence. We give a… 
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