The Rank-based persistence framework and the generalization of topological persistence introduced in [1,4] yield overlapping applications. We discuss the similarities and differences between the two approaches from theoretical and applied standpoints.
Keywords: rank, persistence, categorification, regular category, abelian category, semisimple category, classification, group action, point cloud, poset, bottleneck, interleaving
2020 MSC: 18E10, 18A35, 55N35, 68U05
Theory and Applications of Categories, Vol. 39, 2023, No. 14, pp 444-446.