Interleaved equivalence of categories of persistence modules

2012/10/30 by Mikael Vejdemo-Johansson, Vejdemo-Johansson, Mikael
Computer Science · Mathematics · #06A05 #16D90 #Algebraic Topology (math.AT) #Category Theory (math.CT) #Computational Geometry (cs.CG) #FOS: Computer and information sciences #FOS: Mathematics #cs.CG #math.AT #math.CT #msc:06A05 #msc:16D90

paper · pdf · doi:10.48550/arxiv.1210.7913

9 pages

arxiv created 2012/10/30 · arxiv updated 2012/10/31

Abstract

We demonstrate that an equivalence of categories using ε-interleavings as a fundamental component exists between the model of persistence modules as graded modules over a polynomial ring and the model of persistence modules as modules over the total order of the real numbers.

Related

• Interleavings and Matchings as Representations
• Multi-Parameter Persistence Modules are Generically Indecomposable
• Decomposition of persistence modules
• A refinement of multi-dimensional persistence
• The observable structure of persistence modules