Theory of interleavings on categories with a flow

zbMath1433.18002arXiv1706.04095MaRDI QIDQ4563245

Anastasios Stefanou, Elizabeth Munch, Vin De Silva

Publication date: 7 June 2018

Full work available at URL: https://arxiv.org/abs/1706.04095

zbMATH Keywords

category theorytopological data analysispersistent homologyinterleaving distanceLawvere metric spaces

Mathematics Subject Classification ID

Theories (e.g., algebraic theories), structure, and semantics (18C10) Singular homology and cohomology theory (55N10) Enriched categories (over closed or monoidal categories) (18D20) 2-categories, bicategories, double categories (18N10) Monoidal categories, symmetric monoidal categories (18M05) Actions of a monoidal category, tensorial strength (18D25)

Related Items (12)

Ephemeral persistence modules and distance comparison ⋮ \(A_\infty\) persistent homology estimates detailed topology from pointcloud datasets ⋮ Interleavings and matchings as representations ⋮ Universality of the homotopy interleaving distance ⋮ Thickening of the diagonal and interleaving distance ⋮ Steady and ranging sets in graph persistence ⋮ Exact weights, path metrics, and algebraic Wasserstein distances ⋮ Evolutionary homology on coupled dynamical systems with applications to protein flexibility analysis ⋮ Theory of interleavings on categories with a flow ⋮ Topological spaces of persistence modules and their properties ⋮ The fiber of the persistence map for functions on the interval ⋮ Decorated merge trees for persistent topology

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Categorified Reeb graphs
• Stability of persistence diagrams
• Metrics for generalized persistence modules
• Topological persistence and simplification
• Tree decomposition of Reeb graphs, parametrized complexity, and applications to phylogenetics
• Categorification of persistent homology
• The theory of the interleaving distance on multidimensional persistence modules
• The Structure and Stability of Persistence Modules
• Theory of interleavings on categories with a flow
• Introduction to bicategories
• Induced Matchings of Barcodes and the Algebraic Stability of Persistence
• Basic Category Theory
• Proximity of persistence modules and their diagrams

This page was built for publication: Theory of interleavings on categories with a flow